I, too, have a longstanding problem with cold hands, but have always preferred the dexterity of gloves. My suggestions:
-buy stuff geared towards mountaineering rather than skiing- it's usually better made, too. The best I have found so far are the Marmot gloves (pricy at about $120.00 but really warm); Black Diamond, Patagonia, and Mountain Hardware make good products, too. There was a recent review of gloves in Couloir magazine.
- definitely get a removable liner- one of the things that makes you cold is the liner being damp from sweat. Fleece is great, and primaloft (a synthetic "down") is, too.
- consider a "lobster claw" glove- it's a cross between a glove and mitten. Your first finger has its own compartment, and the other three are together like in a mitten. Added warmth, but better dexterity than regular mittens. I think that Black DIamond makes a pair. Try the Mountain Gear website (mgear.com)
- those chemical hand warmer things work well.
- ski in the west- it's much warmer!! (It's worked for me!)