While Grumpy roars angrily as he roams through the jungle, a small Unicorn pony grazes quietly in a secluded section of the forest. Uncle Jack and Will, apparently on their way back to the Temple after gathering food (they carry long bamboo poles; did they go fishing?), take an alternate route to avoid Grumpy which leads them to the little brown Unicorn. The men are amazed when they spot the mythical creature; they are able to approach it by offering it food. While Will feeds the suspiciously tame animal an apple, Uncle Jack cruelly decides to capture it and take it home as a pet for Holly. Once Jack easily manages to put a lasso around the Unicorn's neck, they are forced to hurry on home since Grumpy is approaching. They manage to flee with the pony and all, but the tyrannosaur smushes their bushel of giant strawberries left in a clearing.

Back at the Temple courtyard, Holly ices a chocolate cake while Cha-Ka watches hungrily. The young Paku decides to dab his finger into the side of the cake; Holly scolds him for doing so, since it is a surprise for Jack and Will. The men return from their trek with their own surprise -- the Unicorn -- and shout out "Happy Birthday!". Holly confesses that it's not her birthday, but her uncle believes it could be since they really don't know what day it is. When Cha-Ka shows off the cake that Holly has made, Uncle Jack pulls a small burning stick from the brazier and inserts it into the cake like a birthday candle. Holly makes a wish and blows the "candle" out; the family laughs merrily as she serves up pieces of the birthday cake. Their joyous celebration is offset, however, when we see Enik marching sternly toward them through the jungle from the Lost City.

While the family enjoys the cake, Holly notices that "Corny", her new pet, is thirsty. She decides to fetch some water, so Will asks her to refill their water jugs and also gather some strawberries. Cha-Ka joins her, but not before greedily snatching another piece of cake, which he stashes away in his pouch. Soon after she heads out, the men are about to tend to their day's catch of fish, but Enik arrives to warn them about Holly's pet. The Altrusian loudly states that "Toki"'a presence in the valley is bad; it belongs in the Land of Snow as the rightful game of the "Tapa". Enik explains that the recent earthquakes must have opened routes from the Land of Snow into the valley; "Tapa" will bring devastation upon them unless the Unicorn is released. The Altrusian commands the men to go tell the children to release "Toki", but Uncle Jack refuses, calling the creature Holly's birthday present. Jack informs Enik that if he wants it released, he must persuade Holly himself. Enik is angered by Uncle Jack's complacent reaction, and stomps off to find Holly after calling the Marshall men fools.

Out in the jungle, Holly reminisces to Cha-Ka about once owning a billy goat, though she definitely prefers Corny's personality. (Cha-Ka claims to be unfamiliar with the term "billy goat", yet very recently [Hot-Air Artist] he claimed to have gotten cream from a goat. Holly also fails to remember that she once owned a horse named Comanchee [The Hole]; apparently the story editors didn't care much about checking for consistency.) She and Cha-Ka leave Corny alone to graze for a moment while they gather some strawberries nearby; while she boasts to Cha-Ka about Corny being smart enough to learn many new tricks, they suddenly hear the Unicorn whinny in distress. They rush back toward Corny, but their pet has vanished; they begin to look around but are forced to flee from LuLu, since they are near the edge of the swamp. Enik arrives to command Holly to free the Unicorn, but she explains in a worried voice that he has disappeared and may be in trouble. The Altrusian urges Holly to forget about the creature, offering her a "toad with a precious jewel in its forehead" as a replacement, but Holly is not interested in any creature that may end up giving her warts. Her attention quickly returns to searching for Corny; just then Cha-Ka discovers huge footprints in the sand nearby. As they all examine the footprints, Enik identifies them as Tapa's, and explains that the beast has taken the Unicorn for food. The Altrusian advises that they leave the area, but Holly insists that she will save Corny, no matter how big Tapa's feet are. Enik loudly warns Holly that her choice is "not logical"; he shouts to her to let Tapa and Toki go free. After Enik furiously marches off, Holly confidently boasts to Cha-ka that they can outsmart Tapa; the two, however, are shaken with fear when they hear the beast's fierce growl.

Holly and Cha-Ka follow Tapa's tracks to rescue Corny, which leads them to higher, colder altitudes. Holly begins to shiver, but Cha-Ka, with his warm fur, doesn't seem to mind the cool air. They press on after hearing the sound of a wild cat.

Back at the Temple, Jack is furious upon hearing Enik's news that Holly and Cha-Ka went off unannounced to track Corny. The Altrusian unnecessarily raises his voice to reply that he warned them, but did not stop, them since he is not their keeper. Enik continues shouting as he warns the men that Tapa is carnivorous, beast, capable of breaking the neck of a brontosaurus. Uncle Jack disregards the warning, replying that they must be concerned with Holly more than themselves. As they rush off, Will warns Enik to "batten down your own hatches" if they have not returned by dark.

Holly and Cha-Ka follow Tapa's tracks to a narrow gorge bridged by a fallen tree. Holly is at first hesitant to cross, but when Cha-Ka wants to chicken out, Holly insists that they continue on. She leads the way across the fallen tree, muttering "don't look down" nervously to herself. (Strange, not only did Holly already conquer her fear of heights, but she specifically did so by looking at the earth [Elsewhen].) The logs shifts while they are half way across, but they manage to make it safely to the other side. They pick up Tapa's tracks, bearing the cold as they pursue the beast; not long after they leave the gorge, the bridging tree trunk falls in.

Uncle Jack and Will head through the jungle tracking Holly; meanwhile, she and Cha-Ka find Corny abandoned on a high plateau. They try to lead the Unicorn back home with them, but Tapa arrives wielding a club; Holly and Cha-Ka are forced to escape through a tiny hole that leads into an ice cave. Inside, they find animal skins and large wooden clubs, so Cha-Ka volunteers to build a fire; Holly, however suddenly realizes that they have stumbled into Tapa's lair!

Will and Jack follow Holly's tracks to the edge of the gorge to find exposed roots and torn earth; they conclude that she and Cha-Ka must have crossed over a fallen tree. Meanwhile, Tapa angrily pursues Holly and Cha-Ka by going around to his lair's normal entrance. The two kids hide behind a large ice pillar just in time to avoid being seen by Tapa, but the beast prowls around the cavern growling loudly since he smells their scent.

Cha-Ka decides to hurl chunks of ice at Tapa, sending the abominable snowman into a violent rage. As Tapa senselessly flails his club at everything surrounding him, Cha-Ka urges Holly to flee before she is eaten. That gives Holly a foolish idea; she instructs Cha-Ka to give her a piece of his cake stashed in his pouch. She claims that the creature, also known as "Yeti" or "Bigfoot", is actually reported to be quite "childlike and gentle". She slowly steps out into Tapa's view, holding some cake in her hand as a peace offering. The snowman at first threatens her with his club, but Holly somehow wins his trust in less than 10 seconds. While tasting the dessert, Tapa momentarily becomes alarmed when Cha-Ka tries to sneak past them, but Holly instructs the Paku to drop his snowball and move slowly toward her. She introduces Cha-Ka to the abominable snowman, but under her breath informs Cha-Ka that they will make a run for it once they move over toward the front entrance. After offering Tapa another piece of cake, they try scooting towards the exit, but the snowman is wise to their plan; the beast's angry roar begins to loosen snow and ice over the entrance. Holly realizes that it may take some time to escape, so they begin building a fire to keep themselves warm in the meantime.

At the gorge, Uncle Jack takes a stag's antlers that he somehow found and ties their rope to them. He explains to his nephew that they will use the antlers just like a grappling hook. Jack twirls the antlers on the rope above his head; he then tosses it across the gorge in an effort to hook it onto a standing dead tree. In Tapa's lair, the kids have started a campfire; Cha-Ka notices that Tapa is afraid of the flames. Holly instructs Cha-Ka to sneak out quietly while she teaches Tapa how to use fire; she asks him to grab a hide to cover Corny on his way out. Tapa is distracted enough while overcoming his fear of the fire that Cha-Ka manages to dash out of the cave with an animal skin. Holly manages to calm and enchant the snowman by gently dancing around and twirling her torch.

Uncle Jack succeeds in hooking the antlers around the dead tree's branches; Will anchors the other end to a tree trunk on their side. Will enthusiastically volunteers to swing across, but Jack selfishly insists on going since it was his idea in the first place. He instructs Will to stay behind to begin the long task of chopping down a tree to serve as a bridge to get back. Jack begins to swing his way across, hanging from the rope by his hands and reaching one arm out in front of the other. Predictably, the knot on the antlers begins to loosen; just as predictably, when it comes undone, Jack falls to the ground on the other side. (C'mon, neither Jack nor Will would be stupid enough to use a granny knot on the antlers. Dad had reminded Will to use proper knots [Elsewhen], so even if Jack made the blunder, Will would have noticed it and corrected his uncle.) Jack signals to his nephew that he made it safely across, so Will begins chopping at the tree with his small camping hatchet.

Holly has worked her way over to the ice cavern's entrance, where she warns preoccupied Tapa not to directly touch the campfire. She manages to sneak out, but the snowman soon notices; he chases after her, flailing his club and roaring madly. His roars set loose the ice and snow above his lair's entrance, causing an avalanche which seals the creature in. Holly meets up with Cha-Ka, who waits holding onto Corny's reigns, and they all rush toward home as fast as they can. Tapa's imprisonment is short-lived, since he uses a gigantic broken-off ice stalagmite as a battering ram to break free.

Jack calls out to Cha-Ka and Holly and manages to find them. Tapa, however, is hot on their trail as they all rush back with Corny to the gorge. Will is just finishing chopping down the tree; he calls out "timber!" as it falls perfectly to the other side. Tapa closes in on them before they begin to make their way across, so Holly tosses the entire pouch with the remaining cake to the creature. Tapa growls as he greedily devours the birthday cake, allowing the Marshalls just enough time to somehow traverse the tree trunk with Corny. Once the cake is gone, an enraged Tapa jumps around and flails his arms; Jack interprets the beasts statement as "keep out of my territory". The abominable snowman grabs hold of his end of the tree trunk and shoves the entire thing into the gorge.

Holly is glad that they succeeded in saving Corny, and hopes that Enik will understand that their risk paid off. Uncle Jack is doubtful, predicting that the Altrusian will call them "illogical", since he just doesn't understand what love is about. When Cha-Ka mounts the Unicorn pony facing backward, Will laughs and slaps at the pony's backside, calling out "giddy up, Corny, let's all go home!"