Going to throw a little fuel on the fire. If its a dry day, you CAN drive on summer tires in the cold, you just need to leave a bit more braking distance and not drive like a fool. I drove my mustang in VA from the start of the college semester through to thanksgiving, on summer tires, and had a few days where it was sub 40 degrees. No issues because I was extra cautious. For the sake of troubleshooting brakes vs. wheels/tires I would do this. Go out at a time with minimal traffic, and drive a few miles on the other wheels/tires and see how it goes.
A stuck caliper CAN cause vibration but it would also cause excessive heat, to the point that the caliper would begin to look as though the finish is rusted (as they can get hotter than the paint/coating tolerance). In some cases, if it gets hot enough, you may also find yourself with damage to the finish on your wheels (chrome bubbling).
If you have a brake issue, regardless of tires/wheels, I would correct that FIRST, as there is no point in chasing other issues when you have a "known bad" part on the car. This is my .02 but brakes and wheels/tires, as well as suspension are some of the biggest safety factors, and IMO should be kept in tip-top shape at all times, as they are your first line of defense.