I've done two Glenmore Lodge courses over the years. Excellent instruction, decent value, lots of cake, readily available access to lots of snow (based in Aviemore). They'll supply technical gear, including boots, and you'll have a much better idea of what to buy for yourself at the end of it. I'd happily recommend them to anyone.
Plas y Brenin are similarly good, but go for their Scottish-based course rather than the Welsh one. Snowdonian mountain conditions are less reliable than Scottish. March is usually a good month, Jan a bit early some years.
There are other, smaller outfits also offering good courses, but I've not used any of them. The advantage of the big two mentioned, is that you're dealing with a reliable, known quality and a spread of excellent, highly cometent staff.
There tend to be a few levels of course. The basic winter mountaincraft ones assume that you're not a climber, the winter mountaineering ones that you have a summer rock climbing background and can tie knots, place protection, set up a belay etc.
As far as gear goes, it depends a lot on what you're doing. For ice climbing you need specialist B3 boots, for more general mountaineering, a slightly more flexible boot can be more comfortable. For multi-day stuff I like plastics because they're warm and don't get water-logged and take ages to dry out like some leather boots - frozen boots, no thanks... But doing a course will put you in a much better position to judge for yourself.
Norway looks superb btw, guess you'll be learning to telemark then?