I usually winter my small new (precious) figs in my little greenhouse and keep them growing ...
If you do not have a GH, winter growing next to bright window will do just as well (beware of them pesty invading fungus gnats).
If you wish, you can also let it go dormant and winter/store it
in some place that stays 'warm' but below 40*F (else it will break dormancy).

Established figs can easily survive freezing (32 - 20*F) temps.
I also had some spare/unwanted 'little' ones that did so too.
Just make sure that the soil does not get 'bone' dry.

Thank you. I will have grow lights set up soon for my seedlings so I may just set it up and keep it growing in the house. I couldn't find anything about doing that so I wasn't sure. This cutting didn't really take off until July so it only has 6 leaves. I may try to start some more cuttings as well.
kim