My rabbits i have right now are outside and the rabbits i had a few years ago were outside to. They did fine Flemish giants are a lot bigger than rex and mini lops. The breeder i got my rabbits from keeps them outside. I have been rotating through alfalfa, timothy and orchard grass whatever the local store has that is green.
I live in town but its so close to farms and open fields only a few houses away there is actually fox burrows in town, and a loose dog. I havent had issues with them trying to get to my rabbits or chickens. If they are going to be on the ground id bury hardware cloth under the ground around the hutch. My hutches are off the ground(mainly because of flooding and snow), but i let them in a fenced area supervised for some time. And plan on building a run i can let them out in eventually.
Since we have gotten the rabbits we have had 2 or 3 storms weekly and they do fine.
Best of luck with your rabbits!