Not only that guys, I would think snow, being one of the best insulations there is it could cause the ice to melt somewhat, as the water is not as cold as the ice, it would take some time but still. I've seen many times where lakes didn't freeze over with very thick ice when there is a substantial amount of snow on it in the early season preventing the cold air to make ice.
Years ago I was ice fishing on Ghost Lake west of Calgary. We had a pretty good snow fall. I was out fishing a couple days before the snowfall and the ice was a good ten inches thick. When I drilled my hole after the snowfall it was about six inches thick and two more days after that it was down to about two or three inches and soft. Scared the you know what out of me standing over 70ft of water. Keeping in mind there was a bit of a current which may have played a part as I was about a kilometer or so down from where the Bow River enters and feeds the lake. I don't know, but It still boggles my mind how quick it melted.