You said the tires were out of balance and that can definitely cause it. Not sure if this is such a "FAILURE" on DT's part either. When they balance a tire, the machine tells them how much and where to place the weight(s), then it either passes or fails after the weight(s) are added. If it were one wheel, I'd say the weight fell off and caused it to be out of balance. There's no point in the worker telling you this either because you'll still see it as their fault (they didn't apply them properly). Since it was two tires, it's harder to say the weights on both fell off, I'm admit.
You asked about the 35º F "cold" weather and no, it has no relevance. I know it's unusual for FL but there are plenty of us who get colder temperatures and for weeks or months at a time.