All I know is ice is weird in my pond. Not much snow on it, and it still blew a hole and leaked water after several days of not getting above 10. The areas I have been plowing are all thick, but the snowy areas (maybe 4") are questionable.
Snow drastically reduces ice growth. It insulates the ice from the air and the water from under will take the ice away. Something you learn with spring ice in the north is to say away from the points that have snow drifts on them. Yes the water is shallow there but its still cold.
If the snow is on the ice in a large mass it will insulate the ice and the water below will melt the ice.
Best ice we had up north was 40"s and my knuckles were on the ice when drilling ice fishing holes. Drilled 14 holes that day and the young guy in the group. Uggggg.