On my screen door, I use a combination of plexiglass ( bottom section ) and "ghetto plastic" ( shrink plastic ) on the top section for winter use. I try to choose where I position the camper so the door side faces south, so I can have some free solar heating/sunshine thru the doorway thru part of the day. It makes it seem more "open" having the sun shine in, and especially if it is a calm day, even though the screen door is not insulated, I still get a net heat gain from the sunlight coming in. My dog loves laying there in the sun by the door....it's a good go for a dog !
And the campgrounds and walking trails are usually almost deserted in winter. It's like having an entire park to yourself.
EDIT: I like state parks in winter because I have electric hookup. Makes it easy to heat with a small ceramic/electric heater.