Well, these are not issues I have in San Diego, but here are some thoughts.
If it has survived two winters (and presumably some before you arrived), then protection may not be an issue, even though it usually is in you neck of the woods.
In colder climates, as I understand it, if you want the cuttings for propagation, you take them in the fall, in case they get damaged by the winter cold. Here, I prune in late January, when the trees finally get dormant. In general, you can prune any time they are dormant, up until bud break. In your climate, waiting till just before bud break will keep you from having open "wounds" on the tree over the winter, where molds and infection are most likely to enter.
You can prune to make the tree smaller (I shorten some of mine by 10 feet every season). You can prune to remove crossing/rubbing branches, open the center, etc. If you are ripening main crop figs, fell free to prune as much as you like. If you are relying on breba figs, pruning is more tricky. You might try pruning half the branches hard and leaving the others to fruit, and doing that on an alternating year cycle.