For cheap gloves check out the outdoors stores like Cabela and Bass Pro Shop. Like this Cabela's: Cabela's GORE-TEX® Thinsulate™ Deluxe II Shooting Gloves
Not much difference between that and a "snowboard" glove.
I personally suggest mittens if it is going to be really cold. There just a lot less surface area to let heat out or water in. Also remember to keep your core and arms warm if you get cold hands. If your core is warm then your body move blood to your hands to shed excess heat and you hands stay warm.