I have a bunch of gear I have removed from various houses and I set up a driveway movie I project on my garage door. I set my projector up on a ladder that I built a custom mount for and then set out speakers around for surround sound. The whole setup process takes less than an hour. The garage door is white but it is also a faux panel door and after a few minutes you do not see the panels, you just focus past it. Your brain is surprisingly good at doing that kind of thing.

The real issue is getting an exterior projector that does not cost an arm and a leg. Talk to your distributor and see if they have any options.