Are you doing short visits? I like Pvt duty because I know where I'll be every day and I know which houses are chilly and which I'm warm in
As far as shoes, I like the rubber clogs found in uniform catalogs/ stores for this weather as long as the snow isn't deep it's really only my toes that get soggy anyway in regular shoes so something like Klogs or closed toe Crocs seem to suit me fine for the walk from my car (usually parallel parked) to the home. If it's especially snowy, I go with boots and a dry pair of slip ins or even slippers for the house. The days I go to school with kids and must wear nice shoes are usually nicer anyway, so I luck out there.