My experience is that dedicated outdoors packs work for school, but school bags flat out suck for outdoors stuff. If it's got a laptop sleeve, it's probably not going to cut it for skiing.
Don't skimp on a bag. Pony up initially, and it will serve you well for a long time.
I've got an old Black Diamond Covert Avalung that's been beaten as hard as I can year round for four years straight. Heavy loads, stuffed full, dragged over rocks, it's been the best pack I've ever had. Probably one of my favorite pieces of outdoor gear. The main zipper just blew out, so I'm going to put in a new one soon.
Osprey, Gregory, Black Diamond, Arcteryx, REI, the list goes on. Check out Mystery Ranch if you're looking for something produced in the US.
If I was going to pick one up right now, it'd be the BD Outlaw. http://www.blackdiamondequipment.com/en-us/shop/ski/snow-packs/outlaw-pack