Here is the problem, I believe. On the winter bike, which is a Salsa Warbird, the part of the thumbs that get cold grip the shifters (Shimano RX 600s) on a metal piece, as indicated by the arrow.
That piece of metal gets cold, even when its inside Bar Mitts, as it is conductively connected to the alloy handle bars.
I am going to try something like this. The foam is the right idea, I believe, but right now it's just attached with plastic tape. I need to contemplate a more secure way to fix it in place.
I'm planning a ride tomorrow evening, and it's going to be cold (maybe 8°F). We'll see how it works....