My horse Ace is being leased at the moment and he is kept in a one paddock at night and then let in a pen that they move everyday so he can have grass until they get something more permanent set up. He has trees and if it's really bad he stays inside at the barn down the street. But he's older and being outside and able to move around really helps with his joints and his stiffness.
Flower is out from for half the day and then in her stall. I really wish we had 24/7 turnout but I do get up to exercise her almost everyday and she doesn't mind. At the moment she's out in a smaller paddock with a run in that she stands in all day, it's adorable. But hopefully soon she'll be able to go were she used to. I think it's 40 acres? I'm not sure. But it's huge and they have to run up a long hill to get to the grass and it really helps with her muscles.
If/When I get my own place, I would keep my horses out 24/7 with a run-in but also have a barn to bring them in for feeding, injuries, and bad weather. I would rather have one than not.