I would pay the extra $20. It's just $20. However, I would be more than happy to leave my horse out any number of nights a week as long as they were in if bad weather was expected. When I had a stall for my horse she was out 24/7 much of spring and fall. She came in during the day in summer when temps were above 90F and she came in at night when temps were to fall below 50F.
I worked at that barn, and so it helped to not have to clean stalls on some of those days for some of those horses. I don't know how much it saved the barn owner in the long run, though.