I will tell you what I do, and what I've done in the past as well.
In the past I had a 4 x 2 x 2 deep, three level cage that I kept rabbits in.
On cold blustery days (and overnight) I tarped the whole thing, on nice days I left it open.
It was wood on three sides, with wire bottoms with pull out trays, and wire on the front. The rabbits did really well in this.
I also made some wood pens out of old pallets. They were wire bottomed and two sides were wire as well. the rest was wood. I would also tarp these when the weather was very cold and blustery.
I do this for a couple of different reasons.
First to protect my car ports from snow load.
Second to provide an extra layer to help maintain heat.
and third, to provide shelter for me going to the feed and hay sheds. (might as well keep myself comfortable).
I do have to deal with frozen water bottles, so in the winter I switch to crocks (bowls)...which surprisingly often don't freeze solid until into January, and during warmish winter days, often don't freeze at all.
- put your rabbit under shade
- keep your rabbit cool in the summer (frozen water bottles help, nice shady tree, constant access to water).
- in the winter make sure that cold wind can not blow up under them.
- in blustery weather make sure the rabbit has some way to get out of the wind. Snow won't bother them but wind on their bellies is a good way to get a sick rabbit.
People who take my advice have rabbits that do just fine for them. And that's just the way it should be. :)