I live a few miles from Honeoye Lake and our lake is in horrible shape , it is a must to have the rain remove the snow and crud ice. I have seen what these conditions can do. It will take forever to get decent ice and that will be questionable ice at best. People think that snow ice (greyy/cloudy ) is good ice, and that the same thicknesses apply to access it safely. Honeoye was very sketchy last year and we had similar conditions, the west side on a lot of the lake never really made good ice, although it was quite cold for many nights. Keep the snow off and we would be fishing on close to 6" of ice by now, snow on and it has not made an inch more in a weeks time of cold temps, -5 here last night. So yes get rid of the snow and start over.