Mystery pawprints left by the Beast from the East

Although we live in a suburban area, we have seen (largely Muntjac) deer on occasions making their way across the roads or down the footpaths. We have never seen a deer in our garden.

I peered outside on Saturday and saw these strange prints. Reason tells me they belong to visiting cats, but they have a distinctive hoof print feel about them with that rim around the edge. However, when I looked up deer tracks, they did not seem to match. If they are feline paw prints, I guess the snow must have melted in a particular kind of way. I wonder what you think...