I also have clay soil, which turns to soup when you mix with pigs and winter. I am having a winter off, from pigs, partly to let the ground recover, partly due to personal circumstance. I never put mine inside for winter, just moved the arc onto fresh ground, and kept plenty of straw inside it, using the old straw to spread round the boggy bits when renewing. If the weather got really bad,ie blizzards, i would put a big bale as a wind break, and they would be draught free. I am considering making a concrete base to put the arc and the troughs on , as I will be having more pigs in spring, and hopefully continue on without a break.
But I can honestly say my pigs are in the freezer for the winter, and very tasty they are.