In reply to Chris the Tall:
I've skied in all of these resorts and did a season in Fernie.
Firstly, I'd echo the sentiments of others, N America skiing is very different to Europe as it is much less sanitised and the ski areas are tiny in comparison. It's also fricking amazing and I would pick it over Europe everytime.
For the resorts you mention:
Whistler is famous and the most European in style (big, good infrastructure, accommodation at the base). I was there last year when they had record snowfall. It was good but not amazing IMO. Worth a visit.
Lake Louise is not as big as Whistler, nor as steep as Fernie. It's got some great bowls off the back of the moutain and good variety.
(nb: If you're going to Lake Louise you can ski Sunshine and Norquay on the same lift ticket. Sunshine is great and pretty big by Canadian standards. Norquay is tiny and only worth a day (plus a trip for the floodlit night skiing).
Fernie is as someone else said, not really for the pistes (which are ok) but the backcountry is incredible. It's a very steep resort and you'll get the most of it if you're half decent at skiing. Weather should be ok mid feb. Powder is awesome in Fernie. You can also cat ski in Fernie which is a cheaper way of doing heli skiing and worth a day if the snow is good (but not too good because the avalanche hazard gets too great).
Big White is quite big by Canadian standards (but not as big as Whistler). I only had a day here and I thought it was very flat. Didn't see much potential off the pistes. Very family friendly resort.
You'll ski everything in Panorama in 2 days tops but it's a good location for doing other wintery things like snowmobiling and heliskiing (v expensive).
My suggestion, if you don't mind a bit of travelling would be to do something of a ski safari. If you fly to Calgary and hire a car you could do a few days in Banff (Lake Louise, Norquay and Sunshine, perhaps also drive over to Kicking Horse for the day) then down to Panorama, then down to Fernie. You could also tag on days at some of the smaller hills like Kimberley, all are accessible. Then back to Calgary to fly home. Fernie to Calgary is 4 hours to put travelling times in perspective.
From my experience the approach is pretty different in Canada so don't be put off by the fact that the ski hill isn't tagged on to the town. Longer distances are par for the course in Canada.
You could put together an amazing trip for 2 weeks flying in and out of Calgary.