I have a 3 month old fuscia cutting. I planted in a pot outside and it's been growing fine. Where is the best place to keep it during the frosty nights so it survives the winter?

Put it somewhere cool such as an unheated room in the house or a frostproof garage. Allow it to get almost dry so it can go dormant.

But it if you think its too immature still to survive dormancy you could keep it on a cool windowsill in the house and let it go on growing very slowly, just enough to avoid leaf drop.

Depends on which variety of Fuchsia [if that's the plant you mean :o) ] Some are fully hardy others frost tender.
either way I would do as Steragram suggests. I keep my non-hardy ones in an unheated greenhouse barely damp.

Winter hardiness depends on where you live - you don't indicate whereabouts in the US you are. Most hardy fuchsias will be OK outside in the ground down to about -5C or even more if planted deeply and well mulched but this doesn't apply to young cuttings! Ask the person who gave you the cutting about next year - you may be able to plant it out next spring.