January tends to have decent weather relatively speaking. Of course as you say it will be short term weather dependent but I find it doesn't get really cold until February. Really cold to me is anything colder than -20C. This year we've gotten a lot of snow out in the mountains but the roads were plowed quickly and the highway was clear to Banff (from Calgary) and then partially covered here and there between Banff and Lake Louise but still manageable. There is a secondary road between Banff and Lake Louise which is open but will be snow covered. The road up to Jasper can close due to avalanches so you can play that by ear.
There's an ice sculpture festival at Lake Louise starting around the 15th of January which you can check out for free during the week (have to pay on the weekend). You can skate on the lake too! Check out Canmore too - it's a little bigger town east of Banff (about a 20 min drive) and has a cross-country facility (Canmore Nordic centre) if you're into exploring the area that way.