How long have you had your lizard? Do you know where he came from originally?
I'm not as expert with Collareds as others here. But I would say that the question of hibernation (brumation) depends on how healthy and well adapted to captivity your lizard is. Some have said that brumation is good for them and rejuvenates them like a nice sleep. Many reptiles can go for surprisingly long periods without food. The key here though is that if they are really in brumation then their metabolism will be way down and they won't need incoming food. If you cool the lizards, I definitely recommend reading Eve's page so that you do it right. But it maybe not really important for you to cool the lizard if you only have one, and no intentions of breeding (which is stimulated by the brumation). It may be better to keep him warm and eating to have some time to acclimate, depending on how long he has been in captivity.
I got my first Collareds in early August this year. A few of them acclimated quickly but a few took a long time. After two and a half months of constant attention, they are just now starting to look like healthy lizards. So I plan to keep mine warm and feeding this winter, or at least most of the winter. Perhaps I may cool them down for just a few weeks later in the winter if I think they are looking good and ready for it. But for now I'm gonna keep them eating.
Some of the hints that have helped me:
1) Give them a soak in some clean water for about 15 or thirty minutes every week or so.
2) Keep some good hide spots for them like rocks and branches to hide under.
3) drip some water from a styrofoam cup with a pin hole in it to let them drink.
4) be diligent about knowing how well they are eating. My boy wouldn't eat much at first but after some wild-caught grasshoppers from my yard, he got jump started and now is a cricket eating monster.
5) make sure the light source is very bright during the day and the temps good, but turn the heat down a little at night and back up in the morning.