As was mentioned above, the amount of snow you anticipate riding in will make a difference. The big thing, i think, is to pay close attention to the hooves before and after your ride to make sure there is no snow or ice packed in. For your bit question, yes, you can ride with a bit. However, some horses will object to the really cold metal, so you may want to warm it up a tad before putting it in your horse's mouth. I will put the bit in an inside pocket to warm up while I groom or just hold it for a few minutes if I'm too lazy to take the bit off the bridle.