I've done both alpine and cross country skiing in Finland. There are generally lots of easily accessible cross country tracks near the ski resorts, but there isn't generally a 'group lesson' vibe like you would see in cross country specific resorts like Seefeld or Dobbiaco. You can generally get private instruction and rent cross country equipment in the Finnish resorts.
The Finns have their big 'ski week' holidays in mid February, before and after that it is generally really quiet on the slopes.
Resorts wise, my favourite is Ruka (Crystal goes there). It's compact, but this does mean that the alpine skiing isn't very big so would be a bit boring for anyone who is an expert. English speaking group alpine lessons. Cross country equipment definitely available to rent, some nice easy starter trails a short walk from the bottom of the ski jump. The usual stuff available like dog sledding, snowshoeing, snow mobile, reindeer farm. The ski area is split into to 2 sides of the hill, interlinked by a gondola and bus so easy to get around. The main hotels are clustered so close to the slopes you can practically ski out the door.
Next is Levi - This is built around a larger town, slightly larger alpine area. Cross country equipment definitely available to rent, some good cross country ski trails near town. English speaking group alpine lessons during the main season. I got there on holiday with Inghams - they used to run until the last week of Feb, but now the last flights from Manchester is feb half term. The usual stuff available like dog sledding, snowshoeing, snow mobile, reindeer farm.. I don't love the slopes at Levi as much as at Ruka, but that's just me being a bit nesh. 2 sides of the hill again, linked by regular buses or you can ski over.
Yllas - Nice downhill skiing but the accommodation is very spread out. The main stuff is in the nearby village Akasompolo, so it's always a bus to get skiing from there. There is a smaller area called Sport Resort Yllas - that has limited services but you can basically go out and ski out the door. Yllas can be really windy so the top lifts get closed, and so you can't ski over the top to the other half of the resort. I still liked it, and the cross country skiing was fine. They did 'taster days' on cross country I think there, might have been organized by Inghams.