I am not in expert in cats as I only owned mine for close to a year. However I have seen a lot of barns and cats that live at barns. I have seen some barns that have really nice places for cats to live in such as club house and an indoor arena's. However most barn cats I have seen have to get through life in cold weather and running away from people and animal. I personally would not want to see a 3 legged cat at the barn as I would not think it will live a good life and probably the chances of this cat to survive a long time is slim. At the barn I board my horses we loose cats and kittens to coyotes all the time and those are the once that can actually run fast with all 4 legs but a cat with only 3 legs probably be the first one caught.
As mentioned above, it might depend on the barn conditions. If predators are not a big problem then I think a 3-legged cat could adapt just fine. I have a declawed barn cat. He was a "free-to-good-home" kitty due to allergies and he was already declawed when he came here. He was supposed to be a house cat, but decided that fresh laundry was a nice litter box so he had to go out. He has done fine out there the past 5 years and he is actually one of the better hunters...I see him with mice all the time. I think they can adapt, but if the house is a possibility I'd go that route first. And if you do put it outside please watch it closely at first just to make sure it is adapting. Good luck!