I think the biggest issue with storing outside is UV. While rodents may be a strong second. UV deteriorates paint and rodents deteriorate wiring. You need to evaluate which issue is greatest. For years my '73 lived in my driveway without any benefit of cover. I also lived in an area that...
Do a search for "portable garage". There are several companies that offer them and in various configurations and sizes. Although I never used one for any of my vehicles I did have one setup for several years as a covered workspace. Mine was from HF and I did have a couple of issues with it...