If I was you in your kind of climate, I will simply tie together the branches which are very flexible and cover each one with a few layers of burlap and place it in the unheated garage since your winters are not sever as you mentioned.
My rule of thumb for bring out the plants are when the local maple trees start showing leaf buds swelling but then watching for the frost forecast because at that time the fig trees are prone to damage by frost.
For watering, watch the pots so the soil does not get bone dry.