For historical temperature records, go to this page on the Environment Canada website, type Banff into the location search box, and you'll get the info you need. It indicates the daily high in February averages, almost exactly, freezing point (0 C or 32 F). http://www.climate.weatheroffice.ec.gc.ca/climate_normals/index_e.html
As far as a brew pub for lunch in Calgary, try Brewsters on 11th Ave SW and about 8th St. SW. It's just south of down town http://www.brewsters.ca
. If you stop in Canmore, try the Grizzly Paw http://www.thegrizzlypaw.com/grizzly-paw-restaurant
As far as lodging goes, since you're out on a holiday and want to have a good time, stay in Banff. There are more restaurants, bars, etc. there, and you'll have more fun. If you were planning on spending a lot of time in the region, then my recommendation would be the opposite. Hotel prices are probably comparable, but the selection is much better in Banff. Winter is considered low season in the region and hotel prices will be at their lowest, so don't be concerned about price. If you were to visit in the summer when tourist traffic goes up about 500%, you would find hotel prices would be about double what they are in the winter. There are definitely good winter deals to be had.
The only place I've ever seen discounted lift tickets are at Costco, where they sell discounted multi-packs of tickets for Sunshine Village and Lake Louise. If you were a local (Albertan) you would be able to purchase a Louise or Sunshine card which would give you a couple of free days of skiing during your time here as well as discounts on the other days, but they don't sell them to vacationers on the ski area websites. Early in the season you can buy them at many sports shops, so you might be able to find them for sale and get them that way.
As far as snowmobiling goes, I believe you would need to leave the national park and find somewhere else where you could rent snowmobiles. I don't know of any place that does, and if you could, it would be a travel hassle.