Usually at the same time. I don't always have cold hands and feet, only some of the time. It has gotten better lately. I don't think it's thyroid because I did a blood test for it. A lot of people have thyroid medication so I don't see how the test could have been wrong, but I suppose it's possible. I know that I sweat 90% of the time when I'm standing up. It will soak through my clothes. I don't know why that is. When I'm sitting it's about 60% of the time, and when laying down maybe 30%. I do use baking soda as a deotorant because the actual stuff makes me smell worse (I assume it combines with my BO and makes an even nastier smell), but that might not be strong enough to actually stop the sweating as it isn't an antiperspirant, it just absorbs the moisture.
The sweat may be from my stress, I have had this problem all of my life so anytime I'm with someone I get worried about the smell. I'm hoping one day that will change.