More snow = greater precipitation = increased water vapor = more evaporation = more heat.
Oh, that's right, according to right wingers on this site, "evaporation" is a "wild theory". Sorry, I forgot.
So, if I understand the logic of this correctely...
If if each of these things equals the next thing
and if a=b and b=c, then a=c,
what you are proposing is that more snow = more heat.
Interesting hypothesis.
Cue the Circus music.