I think for a young person almost any of the AWD 'crossovers" and the like would work, I like Subaru’s, but the Honda CRV, the Toyota RAV4, and the like are good cars (Ford makes one that is nice), I would stay away from the Jeep crossovers, I have heard some not nice things about their reliability.
Folks, with the impreza I don’t think the high insurance is for the standard models, the crosstrek is built on the impreza platform,the high insurance is going to be for the WRX models, especially the STI, which are basically de tuned rally cars. I doubt it is because kids like to hot rod imprezas, you can hot rod civics, you can hot rod hyundais and other ‘low end’ cars, the high insurance is going to be the WRX and WRX STI, so don’t be afraid of it.
One note on cars riding high, while that can get you over higher snow drifts, that also has disadvantages, like wind load on the car, and while they have done a lot of work on suspensions to try and prevent it, the higher a car rides, the more likely it could tip (and it is nowhere near as bad as things like jeep wranglers and some of the bigger SUV’s,crossovers are that high up, but still).
I totally agree with what others have said, about learning to drive in snow and ice and cold rain. AWD is a marvelous thing, as are good tires, ABS, traction control and the modern suspensions and brake systems, but there still is no substitute for good driving (and like some of the others, I went through winters with fwd and with a car now that is real wheel drive, never had AWD). In bad weather, the key rules still apply, sparing use of the brakes, giving yourself larger following distances, as slow as possible steering maneuvers, and the big one, SLOW DOWN. I still see people in SUV’s and the like doing 70 on a highway full of slush and snow, they forget the rules of momentum and inertia, and end up in a ditch or worse. One thing I would encourage the kid is when the first storm they face hits, go someplace (like an empty parking lot) and practice driving, get a feel for skids, for what happens when you brake, if you go out of control, won’t hurt anything, and you learn that way before you hit the real deal.
Depending on your budget, you can buy a certified used car (usually they are coming off leases), or buy one with like 50,000 miles, and the kid likely will get a lot of use out of it. It also depends on how far they will be driving each day, if they have a relatively long commute I would get a newer car, if it is a relatively short commute and older car may be fine.

