A cheap and good solutions is to wear a thin glove liner under a waterproof/semi-waterproof flip-top mitten glove like they sell for hunting. It is a glove with open finger and a cap over the fingers that turn them into mittens, I'm sure most people have seen them. Those kept me really warm while hunting and when I dropped the mitten top I still had gloves on.
Now-a-days I use a differant solution.