I just use regular summer rain gloves on R and L hand and then have those golf mittens with hand warmers in them.
What I've found is that if you keep your core and your ears/ head warm, the hands don't get as cold due to the blood flow.
For core, I can play down into the 20s with just a moisture wicking base layer, a cashmere sweater, and a light wind shell. With only 3 layers, it doesn't inhibit the swing at all and it is amazingly warm. I've tried wool sweaters and other combinations, but this to me is the absolute best tradeoff between warmth and ability to swing freely.