No need to stick with cycling mittens: look around, there should be a variety of relatively water proof mittens available. Look for some polypro glove liners or fleece gloves to go inside the mittens also. I have some mitten/gloves, type that came out a few yrs ago, with full thumb, 3/4fingers and a mitten flap that can cover the fingers and fold back on the back of the glove if it warms up. Good down to the mid 20sF. Doesn't get much colder here though. You don't need hi tech ski, cycle or sport mittens. Less expensive varieties should do as well.
Steve