Rabbit Hutch for Winter Run - Hardware Cloth on Bottom

I picked up a 32"x32""x8' ground level rabbit hutch with the intent of using it for my 3 silkies for their winter run. They are currently in a dog kennel run, but I was worried about trying to weasel and winter proof it. The hutch is not elevated, is solid on 3 sides and has hardware cloth on the fourth side and the bottom. The top is corrugated metal roofing (I will need to do something to keep weasels from getting in the ribs). I plan to attach the run to my coop so that the chickens can get some fresh air and have extra space during the winter (coop is 4'x6'). I'm in New Hampshire, so our winters are long and cold. Should I just put deep litter over the wire or should I put something over the wire to make a solid floor? I was glad to see the hardware cloth on the bottom as it will keep diggers out, but I am concerned about the chickens' feet. I saw some threads that suggested that wire floors are controversial, so I thought I would ask for suggestions on this conversion project. Thoughts?