Stainless can be magnetic, 316 isn't, I think 304 is. Anyway, corrosion is the issue that is being thought about here.
The main issue with stainless is the welding. If the welding is heat treated/beaded or some other stress relief done post welding, then the trailer WILL crack at the welds. If the person doing the welding knows what they are doing and the welds are stress relieved, then the only issue is one of looks. Brushed or swirled surface finish would be advisable to cut down glare, but the metal will be burning hot if left in open spaces with direct sunlight on it. If you do go down the stainless route, have a printer make up some body stickers the same size as the panels in a colour to suit you, your car or where you go ( camouflage?) . This is called ' wrapping' , and is what is used for promo stickers. After about 7 years you will need a new set, but it will cut down the staining and the burning. Your other issue is if any mods or repairs are done, it is harder to find some one that can do the job properly in stainless.
I would go with an alloy trailer with a good wash down after each trip, or just have a decent trailer hot dipped gal'd and be prepared to replace it every 10 years.