In reply to Sanfairyanne:
Your original post asked about winter ice climbing. Scotland can be great for that around mid Feb to mid March but it can be fickle. If you want more reliable ice (specifically, water ice), you might want to check out places like Cogne and Rjukan (great venues but very busy on the easier routes and Cogne can be avalanche prone as well). Plenty of other spots in the Alps as well - have a look at Mario Sertori's Alpine Ice guide book.
But if you're actually more interested in mixed climbing, Scotland is the place to go. Mid Jan to early March would generally be best. Again, often fickle but the good thing about mixed is it can come into condition overnight (might not be very nice to climb but at least there would be something to do) There's mixed in places like Slovenia and the Polish and Slovak Tatras but there's less information about it, the routes are generally longer and you're less likely to find partners.
Booking a course is sensible if your technical skills could do with improving, unless you can find a suitably experienced partner who is willing to teach you stuff. By technical skills I mean the whole range of winter climbing skills - ropework / belays, placing gear in winter (quite different to summer rock climbing), using axes and crampons on technical ground and generally getting around and operating in a winter environment.
So it depends how much you already know and whether you meet the right kind of people to get out with. Good luck!