Lots of good stuff there from Ridge which I won't repeat, but it would seem to me that if you're gonna be starting a hillwalking career in the winter then Skiddaw is a reasonable bet. Unless there's hard icy snow around which would need crampons then it's a fairly straightforward fell by the easier routes. The path is pretty clear so in all but the most severe conditions or with lots of snow it should be relatively easy to follow. You should have a map + compass, know how to use them, have studied your route carefully before hand, and be prepared to change your plans if thing's aren't right.
Having said all that, it is a 3000ft mountain, it's winter, and conditions can be changeable. Good warm clothing - hat and warm gloves, waterproof/windproof outer layer for body and legs, decent mountain footwear with a stiff supportive sole would all be needed. I'd take a torch, a map and compass, food and drink, a whistle, a camera, an extra insulating layer of clothing in a waterproof bag, a small selection of first aid items, plasters and like, and an emergency bivvi sack. Above all don't underestimate how tiring a winter walk can be be if you're not used to it. Make sure you're well fed the night before and not dehydrated!
Very snowy or icy conditions should rule out an ascent for the inexperienced, but there's plenty of alternatives in the Keswick area.
If you're in any doubt about your judgement of the conditions when you visit just pop into Needle Sports in Keswick and ask Trevor!
Enjoy
Ian
www.mountainfreedom.co.uk