Everyone is very quick to say that fabric airplanes will turn to dust if left outside but sometimes that's not the case. It all depends on what type of fabric and paint is on it and how well you take care of it. Modern fabric with aerothane type paint can actually do pretty well outside. The killers for fabric is moisture, contaminants and the sun. You can actually have a fabric airplane last quite some time if you fly it often (keep moisture from building) and wash and wax it a lot. Washing to keep contaminants out of paint and wax to help with UV protection. You could also get covers for it, however covers can sometimes do more damage than good as they can be abrasive to the surface.
If you have old fabric with dope or something that is more porous....that is a diff story.
There are fabric airplanes all over Alaska and other parts where hangars are hard to find and they do alright. Also....how much if your hangar going to be? Probably several hundred bucks a month. Modern fabric and paints can last 10 years outside easily if taken care of well vs 30+ if in a hangar. Lets say your hangar is 300 bucks (mine in FL would be 500)....after 10 years that's $36,000 in hangar costs alone which is most likely well more than the value of your aircraft and certainly enough to get it recovered.
So it is easy to just say "hangar it or it will be worthless"...but that is simply not the case. For some people they are buying an older fabric airplane because they are fun, cheap and maybe can't afford a newer aircraft....but a 300-500 hangar payment will easily push that over the edge of affordability. So at the end of the day the question is do you want to fly or not?