I just realized one interesting difference in the way ice physics is handled in action versus puzzle games.

In both types of games, when there's ice physics present, when you start moving and release the direction, you don't stop immediately, but instead stop some distance later. But what differs is in how input is handled during the time it takes to stop.

In an action game, while sliding on ice, you can press the opposite direction to slow down, or you can try jumping or crouching, or perform any number of actions.

In a puzzle game, on the other hand, once you start moving on ice, you can't stop. In some games you'll stop after a certain distance (if you don't hit anything along the way), while in others, you'll keep going until you hit something. (Note that, in some cases, you may be able to place an object on the ice in such a way that it stops your movement, allowing you to enter a passage you'd otherwise pass by; figuring out how to do this is part of the puzzle.)

As for other genres:
* RPGs, at least the games I consider to be RPGs, behave like puzzle games if there's any ice puzzles in them.
* I'm not aware of any strategy game, whether turn-based or real-time, that has any sort of ice physics.
* In adventure games, all interactions are scripted, so there's no ice physics in the mechanics. On the other hand, the game might dictate that certain things might happen if you try to cross ice, possibly requiring you to have a certain item or something to pass safely.
* Sports games aren't going to have something like ice unless the game is something like hockey.
* Racing games I would expect to behave like action games; if there's ice, I would expect it to be harder to stop or slow down on the ice.

I think the difference is based on if the game gives you time to plan out your movement.

If it does, like in a strategy game, you are expected to commit to it. But in an action game you have to think very quick on your feet and don't always have time to plan. Therefore it makes sense to give the player additional options to deal with the slipping.

I can't name any titles, but I'm sure some games have something implemented.
If nothing else, then how many steps can a unit move in icy hexagons or something. The Secret Files of Tunguska is a good example where there are some puzzles involving ice, but the physics is completely wrong. It's an enjoyable game mostly, but annoyingly illogical at times. That really depends on the game?
I can think of some sports games that had ice in them, not particularly good physics though.
In the Epyx classic game World Games, one event was jumping over barrels on ice. Yeah, that would sound logical, at least if the game is even attempting to model physics realistically, and not all racing games do that. There are at least some games which have winter rallies in them or something similar.
Obviously most racing series don't even start in icy conditions, Formula 1, IndyCar, and so on, so there's no point to model ice in them.

If all else fails, there are winter mods to My Summer Car game. :-)
https://www.nexusmods.com/mysummercar/mods/870


Are there any flight sim fanatics here?

Maybe there is some interesting ice physics in flight simulators?
Ice forming on wings, landing on icy runways, flying service flights to Antarctica, and so on.

Worth noting that snow is not the same as ice. If anything, in snow there would be more friction, making it easier to stop (but harder to move faster), while the reverse is true for ice. (This could make a course containing both snow and ice sometimes tricky to navigate, as that's another thing to keep track of; you want to be on ice in order to move faster (assuming the strategy is to go fast, something that isn't always the case in these game), but snow might be worth it if you've reached a turn or don't want to go sliding out of bounds.)

Warcraft 3 itself only had ice as background doodads.
The built in map editor, however, allowed ice to have different physics. Though in practice it only had 2 sorts. The ''you stop after a certain distance'' was never applied.

1.) Ice skating. Allowed you to control yourself on ice. Add a script that makes the character change colors like disco lights and go skating - beauty! :'') (Like literally -disco on and groovy the ice mazes)
2.) Ice shooting. Aim & go. Hope you aimed well.

I just remembered a true niche game, Pro Pilkki.

Ice fishing on Finnish frozen lakes.


https://www.microsoft.com/store/apps/9nblggh4rxl5


(Yes, there is an audience for that too!)