When is it better to root prune container figs?   Once they hit dormancy in the fall, or just before spring?

Hope some of our expert container growers comment on this.

IMO it is better to root prune and re-poot  in the spring just before they break dormancy and as you are moving them out of storage.
My reason is that if you do major root pruning and re-potting in fall the trees would then sit for months with wounded roots and maybe more wet than they should be for winter storage and could risk health of the roots.

In order to minimize the chances of shock, I would not do any fig root pruning unless the tree is totally dormant.
I prefer to do it around February at the same time during regular pruning.

I would agree with February as well.  For my zone, some of my potted, winter-protected trees tend to wake up in Feb/March.

Thanks for the info, I'll wait till Feb/March.

But the comment about pruning the limbs at the same time. I usually prune in November so I can make cuttings. ....is that the wrong time to make cutttings?

How does it affect the tree?

No, you may take cuttings any time.  You can prune it to the ground if you want.
But root pruning is different.  It is critical that you root prune while the tree is dormant.  Ensure you balance the tree by removing 1/3 - 1/2 of the top growth.

As above so below. I talked to a citrus guy who was losing a corner of the tree for no reason. He lifted the pot and found a pocket of worms eating his roots, roots that corresponded to that section of the tree apparently.