Where you live, you should not have any problems. I have an 88 that still has the original exhaust with no rust. It is kept inside all the time. I did buy a 77 GL 1000 that has sat outside for most of it's life in the desert. The exhaust is still in fine shape without any rust.
When I lived in PA and would winterize my bikes, I would cover the ends of the exhaust with cling wrap and secure it with rubber bands. This would keep excess moisture out. This was in a winterizing book that Honda put out years ago. Never had any problems with my exhaust rusting out.
2012 GL 1800
1988 GL 1500
1977 GL 1000
2012 KLR 650