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Me and my buddies like to climb the Scottish mountains in Winter. Absoloutely fucking beautiful, Icy and snowy conditions in good weather are just gorgeous and being out in the wilderness really turns otherworldly.
As has been said you're gonna want to get a good clothing layering system and it's worth spending a bit o cash. You don't need the newest high tech gear from Arc'teryx but a good merino baselayer for up (and bottom if it's real cold), a good synthetic or fleece midlayer, quality durable synthetic (I like softshell) trousers and a breathable durable hardshell, both jacket and trousers. Goretex or eVent is worth investing in!
You'll also want a warm insulating layer. If it's quite a dry climate where you live get a good quality down duvet jacket for rest stops etc. Sweat you work up turns to icy clammy dampness very soon when you're sitting down for a rest. If it tends to get wet and changable in your country's Winter (like here in Scotland) get a synthetic insulated jacket because when down gets wet it's a bugger to dry it and it ruins it. Also good warm hat and a few pairs of spare socks gloves (including one woolen oversized pair for warmth when wet, I like Dachstein mitts because theyre super cheap and cosy.)
Also yeah bring the appropriate gear with you for getting stuck out if it's a long Winter daytrip, night falls fast. For this reason as well, working on your fitness is good to get where you want to go before nightfall and also because trudging through snow or XC skiing is tiring. As you know already.
Sorry for the long post, I just really love the /out/doors in Winter!
pic related, a picture I took of one of my friends up a mountain called An Teallach in Winter 2011.