Ski
I do have a friend who finds she usually needs a little more replacement hormone in the winter months. We don’t have a good explanation on why, but her body responds better in winter with higher levels of thyroid hormone in her bloodstream. That’s not exactly what you’re describing ~ it sounds like your symptoms come from being too cold ~ so I’m not sure that applies.
It’s tough not to pin all of our unusual symptoms on Graves’ after it’s come on (for so many reasons, not the least of which is that the symptoms are all over the map for different people), but that may not be the root of the problem. It’d be a good idea to talk with your doctor about this, and don’t let them say "oh, it’s not your thyroid, go home." Follow that up with "something is not right, and I need your help to find out what it is. Can you think of anything else we should test for, or another doctor you can refer me to?"