Most of that snow won't last until spring, thaws, sublimation, etc. take it away before it is a big factor.
But here's the good part, gentle slopes lose more surface mass and make some coins more shallow or easier to pick up. The more severe the slope, the easier the pickins after a good winter's washing.
I'm one of the heretics that holds to the notion that wet ground does not help with depth. But that's just because I've dug my deepest clear targets in bone dry ground, time and again. Wet ground does enlarge mineralization effects on signal quality I think, and may help on intermediate depth targets (5"-8" coins) if you're swinging over otherwise clean and lowly-mineralized ground.
Try this, while the ground is still frozen hard and deep, get a few clear patches in a nearby park and check for targets. I've found a few places where the frozen ground gave me excellent reads on deep targets but later in the spring, when the ground was soft and wet, nothing, again later in the year, bone dry, the targets came up faintly. We're talking the 10"-12" deep coins in my neighborhood.
Might be in those spots the frozen ground really decompressed later when it was wet and made the targets just a bit deeper, then compressed again as it dried and compacted back down, elminating the increased effects of mineralization as well. Might be, but no good earth science in my background, just the experience I've had over the years.