I got some of those GIYO Bullet handlebar mitts that Shinobi_77 recommended for trying out.
No real-world experience in the cold yet, but a few additional pieces of more general info. Being rather huge slabs of 5 mm neoprene (it really is that thick) ... yea, the stated weight of roughly 300 g is very real. With the mtb version, you may have to restrict the amount of clutter on your bars. I assume, most brake levers and shifters would work OKish, but more than that might be a stretch. With a little force, I got them past Magura MT levers and very short inner bar ends, kinda works, but it's definitely on the tight side.
As for
getting in/out in a hurry (especially getting out in a matter of fractions of a second because unforeseen crap or signalling in city traffic)
I don't think that's much of an issue with these. The mouth is fairly wide and has no cuff - so as long as you remember to pull you hand back first (instead of moving to the side), you should be good.