To my knowledge there is no ArGIS model thus far that could accurately render an "average" snow cover for a given location. But i could very well be wrong.
One of the key problems with studying snow is the extreme spatial variability. The main factors to take into account are a. actual snowfall (varies greatly w/ orographic effects, b. elevation, c. wind erosion/deposition, and d. slope aspect, and e. slope angle; and there's a host of other factors as well. It's quite the complex problem, and the relative influence of said factors varies greatly mountain range to mountain range.
There's certainly been a lot of work done on this, but no "quick fix that I'm aware of. Check out past
ISSW proceeding and journals of hydrology/glaciology.
Without local knowledge, I've found the best way to approach this is to find an photo taken at the time of interest, then use it to manually digitize snow-covered areas. , using a bit of artistic license as necessary to achieve the desired look. I draw a polygon covering the greater snow-covered area, then cut out wind-stripped ridgelines, steep faces, sun-melted slopes, etc. Probably not the answer you want, but it's worked for me in small areas of interest.