We have some firm snow out as I type this. I have had good luck going through snow up to 3 to 4 inches deeper than the bottom of the skid plate between the front wheels. More momentum will get you through deeper drifts, ice underneath will stop you soon after the skid plate starts to drag.
When it was powder, I could blast through drifts waist deep.
Rule of thumb...a 4x4 ATV will go through at least as much snow as a 4x4 pickup.

 

My 400EX would go through about 6-8inches, spinning like crazy the whole way.

 

Well i wouldn't think snow would add up that much on a lake but, i notice you have a winch so i would recommend you get about a half inch round piece of metal bent into a ring at one end and have the other end twisted so you can screw it into the ice. This will give you a place to anchor. they make these somewhere but i forgot where. sorry, but i hope this helps ya.