In reply to geomickb:
I started as a student joined the climbing club, then just went on a winter trip with a (slightly) more experienced mate.
I used the same kit for winter climbing as did for winter walking, and borrowed crampons and axes. For grade 1 you'll only need 1 axe and crampons in addition to what you already have (rope etc)
There's loads of good books (Scotlands Winter Mountains for instance) and the obligitory you tube tutorials but nothing beats your own experience.
My only advice would be to set the compass for your descent before starting up (assuming normal winter conditions).