If you haven't already read it, please read Frog Forum - Gray Tree Frog Care and Breeding

It has info on hibernation, see the bit on 'Cycling' under the 'Breeding' section. Especially the bit about not feeding before putting them into cold storage if you opt for that route.

In the winter I use a 40 or 60watt incandescent bulb on the top of the tank as my place gets pretty cold in the winter. It gives off enough heat to keep my frogs up and active. As long as it stays over 18C or so (About 65F), I find mine stay active. Probably some added heat and moisture will convince yours that winter is over and spring has arrived if you want to try to keep it active over the winter. Also make sure it has lots of hiding places up high so it doesn't feel as exposed when it comes out of the ground.

Mealworms are fine as an occasional food, but gut loaded and dusted crickets are a fine staple. Earthworms work great as well. Or roaches if you're allowed to keep them.

If you have a warm day coming up, it would probably be fine to set it free now near a suitable refuge. They winter under leaf litter, or under logs, tree roots, things like that. Often near the surface but under a bit of cover.