The cold weather can damage your skin, particularly the skin on your hands. When you are outside in the winter, make sure you put on a pair of gloves. In particular, either cotton gloves or leather gloves will work the best. Stay away from wool gloves, as they may hurt more than they will help you.
If you are getting ready to put something on your skin to moisturize it, like an ointment or a lotion, make sure you get your skin damp first. That will help the moisturizer do its job. It may be best to apply the product within a few minutes of getting out the shower or the bath. Simply pat yourself dry, so that you are not dripping wet, and then put the product on.