If swapping tires on the same rims is a hassle, because of run-flat tires, then the obvious answer is to mount snow tires on a second set of rims for winter/mud season.

Also, FWIW, I have a Chrysler Pacifica minivan, but mine is just the standard front-wheel-drive gas-powered version. No hybrid or AWD. And my van doesn't even have a spare tire at all. It has a can of tire puncture sealer and a little air compressor I can use to apply the sealer and re-inflate my tire. So even standard vans don't all have spare tires, even without run-flats.