I agree with Brad, this time of year is a little scary to put any type of bird outside just off of the heat lamps. If it was me I wouldnt do it. I'd just start moving the heat lamp a few inches higher away from the chicks every other day (if this was me) until it's so far away that the quail have to huddle to keep warm. But i'd keep them in the garage over most of the winter if it was me unless your outdoor cage/pen/hutch has a shelter area that completely blocks out the wind.
When I put my quail outside they were 4 weeks old, however it was too hot in my house for them (they were actually panting) so moving them outside they actually enjoyed the cooler weather, it wasnt too cool somedays it still go up into the 70s but the nights were cool. My quail molted twice after i put them outside, so imagine how cold your quail would be if you put em out and they started to do the molts im talking about not too good i'd say!
What i'd do too after i took the heat lamp completely off the birds is pick one up and flip it's feathers up to look at the quils of the feathers if they are dark blue (like ink) in color then that's their blood feathers, it means their feathers aren't fully in yet and they aren't fully able to keep themselves warm enough to combat really really cool temps. Again id ont knwo what OK is like temp wise, but i wouldnt put four week old quail in anything lower than 50 F if i could help it.
DO what you think is best for your birds and what works for you but just be very realistic about the temps and their feather development is all i can say.
I have my quail in a very large rabbit hutch, it has a large outdoor wire part, and a nice sized indoor part (basically like a built in dog box) I then put a heavy duty tarp around the whole thing almost down to the ground of the legs to keep a ton of drafts from flying up through the wire floor of the outdoor part. They're doing wonderful in it...however I "winterized" them as many say. I'd love to raise more coturnix quails this year however i stopped after my last batch because I would be really scared to put any more birds outside this time of year but that's me.
Hope this helps give you some considerations
niki