Welcome to the yurt forum!
1 foot is not a lot of room to move around under the yurt, so it is going to limit you a bit. From what I understand of spray foam
, you need much more clearance to apply it. So that is out. If you can actually fit under there, you might want to try some hard foam insulation? It is going to be tough though.
At this point, I see your only real option is rugs, or if you are on the grid, you may want to look into electric radiant floor heat. I have seen this done on TV, never live, but it is pretty simple. You would have to put some sort of floor above it, like a floating floor, wood, etc.. I find most people in yurts don't want to use a lot of electric so this may not be an option for you.
You could also do a liquid radiant heat, as long as you have a heat source, but this is still going to be pricey.
As for mice. I get them sometimes UNDER my yurt camp, which has at it's lowest, a 2 1/2' clearance, highest 4' clearance. They have yet to actually ever get inside though. Honestly? The best solution there (short of using poison) is a cat or mouser type dog. My Jack Russel terrier terrorizes the mice. One day he killed almost 10 that had made a home in a tarp I left under the yurt. It was a slaughter.
I hope that helps!