Those are poagies. "Bar Mitts" is a copyrighted brand name and product, which in my experience didn't work well until I took the trouble to make substantial modifications to them.

I tried heated gloves from "cozy winters" but they were made for average size hands... meaning that that the sell is in denial about their sizing information. I returned them for one size larger and they still did not fit.

I am now thinking that what I need is wetsuit gloves inside my snowmobile mittens.

Arctic mittens are much too warm and not water proof. I live near Seattle, it may get a little colder here. down to 20 degrees?

But the wet & wind makes 35 degress unbearable.

If you buy any neoprene or any other stretchable gloves check the fit as stretchable gloves usually restrict blood flow making fingertips colder than usual

I don't know if the OP is still reading this, but for the benefit of european riders:

Aldi are stocking ski gear, including mitts.

These are very heavily insulated on the backs, including the thumb. Only had chance to try them once, in foggy 2C weather. They were far far too warm for those temperatures. Should be good for -5C and below.