Snow /Ice levels generally fall into these sets of design tropes.
1. Taking movement control away from the player. Slippery surfaces or snow slowing you down, it's the worst part of games like BotW which focuses on freedom of movement and the like, and generally all platformers like Mario.
2. Enemies stun you for longer periods of time. Compounded on point 1, more freedom is taken as enemies are an even bigger pain in the ass to deal with.
3. Lowered visual acuity/blocking of vision. Navigation and planning is more difficult as Snow either blocks your vision or lowers the draw distance viewable.
Btw the problem with them in BOTW isn't even the mobility or anything, it's that they all have the same music and stuff. There isn't much differences between each of the several snow mountains in the game
Snow levels/environments I absolutely love when done right. Uncharted, AC III, and Rise of the Tomb Raider are some examples.
I love when they actually make snow look and feel like snow, where deep snow makes your character move differently in it and the snow itself moves around as you walk through it.
It's nice having different environments and variety within them imo and thats what a well done snow environment can do.
I hate when games have "snow" and then simply put a flat white texture on the ground and have 0 impact on the actual gameplay in terms of movement or other things, it makes the whole thing feel frivolous (IE Skyrim).