Not fammiliar with your climate, but here i regularly see late figs hanging on the bare trees. If i am not mistaken breba crop grows along with the first vegetative growth, the figs do grow faster the first leaves but they are always growing together.
Here in fall and in winter, in Sofia ive seen trees full of figs, those are eather late figs or caprifigs. The caprifigs are the male figs, in which the fig wasps stay trough winter.
Capris ive heard do not ripen like regular figs and just stay dry and basically unnedible, if the plant that you found doesnt produce an edible fruit sometime next summer, theres a chance it is a male caprifig.
By the way i dont think that cold makes figs sweeten up, guite the opposite! With my fig i just stop harvesting whats ripening on the plants after 15-20 of september, the fruit is just not sweet and rather bad tasting if ripened in cold temperatures. Energy for fruit development mostly comes from leaves, i guess figs are kinda an exception with their breba crops, which i think are nurtured from the plants stored energy, at least until the first leaves start to photosintesize.