I just park mine. My parking area is pea gravel, and on the north side of my garage (outside) a little protected from the sun during the low season. That's it! It will sit for 6 months or so most likely. I haven't had any problems with flat-spotting. Its a cold winter with snow and ice, so maybe that helps? Hinders? Beats me. I've heard to just move it a few feet every few months to rotate the tire and change the flat spot, but I never seem to get around to it.
Not tire related, but I do keep the 12 volt battery charged through the winter and bring in electrical items like flashlights, co detector, water pumps, portable lights, etc.
I think the best solution is just to take a couple of winter camping trips someplace, preferably warm where there's no snow. "Honey, I need to go to Arizona for a week or so to take care of the tires on the trailer!"

"I'm going to the west coast for a few days to get rid of the flat spot on the trailer tires."
