Hi gregmartin,
IMO, no, roots don't grow the whole winter - I was wondering the same last year, and did a test .
But, roots will start to grow let's say one month before the buds do break - This is the time when I start the fertilizing program on my figtrees.
So if you want your tree to grow stronger next Spring, pot up in the Fall. Just don't raise the temps, for instance by keeping the tree in a greenhouse, or the
tree might get tricked into making new growth in the Fall.