Hans not appearing in this short like in "Frozen Fever" is fitting when you tie in with "Coco's" theme about remembering: he's been nearly forgotten.
True to the Rule of Symbolism, whenever Elsa uses her ice powers by taking one step, it represents something monumental happening because of one small thing (freezing the fjord causing eternal winter, building the foundations of her castle, etc.). So when she uses her powers to create an ice Christmas tree, it represents how one small thing (Olaf) created a new tradition in Arendelle.
One of the traditions that Olaf collects looks like the Gävle Goat, which is famous for being burned down each year by arson. How does the sleigh catch fire? When a coal from the sauna lands in a pile of Gävle Goats.
In many ways, Elsa's impromptu party at the end is the exact opposite of the surprise party at the beginning. It’s outside rather than inside; in the night rather than the day; impromptu rather than planned; it embraces everyone’s traditions rather than competing with them; and it features the whole town actively seeking Olaf, rather than Olaf imploring everyone to stop leaving.
Speaking of opposites, Elsa’s stomp to create the ice tree is the same move she used to build her ice palace in "Let It Go," but with opposite intent. That palace was all about keeping her isolated, whereas the tree is about bringing everyone together.
Olaf says he is visiting every house in Arendelle, but he doesn’t visit the ice palace where Marshmallow lives. Considering Olaf and Marshmallow were brought to life within a day of each other, Olaf probably realised that his brother wouldn't have any traditions yet either, since it's his first Christmas too.
Because Olaf symbolizes Anna and Elsa’s connection, it’s no surprise that Elsa slamming the door in Anna’s face — his symbolic opposite — upsets him and spurs him to action. It also explains why, when Olaf knocks at the first house, he uses the same shave-and-a-haircut knock that Anna used on Elsa’s door in “Do You Want to Build a Snowman?” On top of that, it shows in Olaf's contribution to the Yule Bell ringing, where he pulls down on the end of the rope, just like Elsa did back in the day.
Olaf's flurry being missing even when he's indoors, despite one scene indicating that he doesn't have his permafrost yet and is still susceptible to melting. Elsa's powers are constantly growing, and they could have reached a point by now that he's heat-resistant enough to withstand the temperature of a the average Arendellian home (or the castle) in the winter, but not yet enough to withstand all heat.
A bit of "Fridge Heartwarming" - when Olaf is found in the forest, several of the townsfolk present him with replacement versions of their traditions from earlier (candy cane, huge scarf, Gävle Goat, among others.) A subtle way of showing how thoughtful everyone is; having shared their traditions with Olaf earlier that day and then been told he's missing, more than one villager realized, "if he's missing, he probably lost the stuff we gave him, so let's bring more so that his mission isn't a total dud when we find him."
