Since different classes have different tires, I'm not aware if anyone has a complete list (gtplanet may have). It might make it easier if you let us know which specific car/class you are working with first to talk through those tires.
Ice tyres = Use it when there is snow on the track or ice tracks
Wet tyres = Use it when it's raining or snowing (Thunderstorm, Blizzard)
Snow tyres = They are useless, no good grip in any condition, i don't know why, but they just doesn't work.
For road cars that don't have "wet tyres", under raining or snowing conditions you must use medium or hard standart tyres, it replaces the WET tyres.
For some reason, the SOFT standart tyres gives you much less grip than medium or hard standart tyres.