I can't speak to mulching figs, because all mine are in pots, and not in ground. I can speak to mulching in general, both summer and winter.
I mulch my elderberry shrubs, and most of my apple and pear trees. All the reasons you've given above are true. And summer mulching helps keep weeds from competing with the trees for nutrients.
I use leaves from all my maple and ash trees, I have many. It keeps down the weeds, adds nutrients to the soil, and protects in winter against freezing/thawing. If we have a good amount of snow here, on top of the mulch, that insulates the ground even more. The problem I see is not the ground freezing, but freezing then thawing, then freezing again and again.
The more mulch you can heap on it, the better it will work. Just keep a small ring of space right next to the trunk, so the mice won't gnaw on the bark. Bark will work, or old hay, or leaves.