Yes, just make sure that they are out of the wind and that they don't get wet. Mine have a pen that is 1/2 completely enclosed and the other half is closed on 3 sides. I've lost a few this winter (with this unbelievably crazy weather this season!), but they usually do just fine. You can cover their cage with a tarp if they are outside, or give them a box to crawl in to snuggle.
Well, it was -2 F here yesterday morning, and at 8:30 am, my Coturnix were happily eating, playing, and doing the same exact thing they do every morning. They didn't act like the temperature made much of a difference to them. I threw some day old bread in there for them as a treat, and that was the big excitement of the day. The weather, well, they weren't impressed. I have them in what is essentially a greenhouse type structure this time of year, completely closed except for one end for fresh air, which has sort of a covered canopy over that to keep out precip. When the weather warms in April, I will remove the sides for air flow, and put a shade cloth over the top to block the hot sun.