I'd prefer to keep them out 24/7. The cougars would be a problem (are there any dogs on property that could make some noise?) but I don't think the weather would be. A horse can stay warmer easier out of a stall. Depending on how her coat is, you may want to put on a sheet if it starts to get wet/windy/cold, but I can normally keep mine out and they're fine.
As far as keeping her stalled, I don't think it would be a huge deal, though I'd want her to have lots of things to keep her occupied especially since I'm guessing there wouldnt be any horses in other stalls she could see/talk to?