I see canvas covered steel pipe framework "run-in sheds" advertised. Compared with most designs they seem "flimsy", but they would fit the need from my my "philosophy" of what a run-in shed should provide.
Then again I am not a horse person.
Currently where my daughter boards there are no run-in sheds, but there are fence rows where they can get out of the wind as well as shade.
Do you folks think these "flimsy" sheds will work?