Quick I have seen both dug out to the dirt beds and then deer that lay right on top...same ridges same day of scouting, I have a bunch of photos of this at home I will dig through them and post some tonight when I get home from work.

To answer your question I dont think it random, some dogs just like to lay in the dirt while others are content to lay in the grass, I think deer are the same, some like to dig down to the dirt while others are content with layingon top of the snow.

Btw, how deep was the snow you were seeing this in.. ? I notice the mix of dirt beds to snow beds to be about the same when the snow is between 3-8 inches deep..

If you want to know if its a buck or a doe, smell it. Especially from Late Oct to late Dec