As in most northern hemisphere locations February tends to be the optimal month in terms of being late enough for decent coverage and early enough to avoid spring conditions except for locations with bad exposure.
So I generally tell people in January to pick a high snowfall area for coverage and in March pick a high altitude well exposed area for surface conditions. In February you have more leeway to consider other things like terrain, resort ambience, etc. In Europe you do have to worry about school holiday crowd issues, particularly British and French for France and German for Austria. Find out which weeks those are before booking.
I have minimal snow data for the Alps. By word of mouth the Arlberg in Austria, Andermatt in Switzerland and Val d'Isere in France have high snowfall reputations. But in the Alps that means 300+, not 500 like ALta and Targhee.