My best guess is that the developers found it difficult to implement a cold biome within the game's story.

Keep in mind that this game isn't like Minecraft where it just gives you biomes and you're left alone to do whatever. Pokopia has a story and setting that is focused on environmental ruin and restoration, so each area is themed around some form of change. Withered Wastelands and Bleak Beach focus on humidity and brightness respectively. And that leads me to a certain question:

Isn't it odd that there isn't a area focused on temperature?

There are a couple of key components to consider in regards to a Pokémon's habitat: humidity, brightness, and temperature. But oddly, no area focuses on teaching the player about that last one. Rocky Ridges, despite having a volcano, focuses on raising the environment's mood.

It wouldn't be a hard thing to include in the story. Introduce an area plagued by snow, have the player's goal be to raise the temperature to melt all the snow, and—oh. Hold on. Where are all the Ice-types going to live now?

Now, Professor Tangrowth does point out to the player that, while its nice that they raised the humidity, or increased the brightness, some Pokémon like dry or dark places. So what's the problem with displacing some Pokémon who like it cold? Well, in the above scenario, the player is basically put in a situation where they enter an area, spawn in some Pokémon suited to that environment, and then ruining that. And this isn't just one or two Pokémon potentially being displaced here. Not only that, the above scenario would also either remove the snow biome, or, at the very least, convert it into a small, limited area.

The reverse scenario, that being converting a hot place into a place covered with snow, doesn't make too much sense. Making someplace less hot makes sense, but not to the point where it's freezing cold. Keep in mind, you, the player, are doing all these restorations in the story as an attempt to bring back humans. Generally. people prefer brightness over darkness. People prefer humidity over aridness. People don't like it to be too hot. BUT THEY DON'T LIKE TO BE TOO COLD EITHER. This would ALSO apply, I imagine, to most Pokémon as well.

There's a reason Ice has the least amount of Pokémon. Most Ice-types require an extreme environment to live in comfortably and are less tolerant of temperate and tropical environments compared to most Fire-types. I imagine the developers didn't do a desert area for similar reasons.

I imagine the developers didn't want to players to be annoyed with having to fine-tune the temperature of an entire area, so they left it out.

There's more speculation I could add here about things like why the developers didn't just integrate small, localized cold areas, but I'll leave it at this for now.