Subarus hold their value like crazy right now.
You're not going to find a decent 2010+ for $15k unless you're OK with 80k+ miles...and even then...it might be difficult.
Same thing with a Honda.
Hyundai's AWD system kinda sucks; they are not that great in the snow IMHO compared to other manufacturers.
You might find a used Ford Escape or older Nissan Rouge for that money.
What I do is lease my wife a new AWD SUV every couple years. She pays it and its usually around ~$200/month.
No worries about wrenching, buying tires, brakes, etc... If something goes wrong, she takes it in and gets a loaner.
It's just easier that way and the savings seems pretty minimal vs. buying something used and then putting time and money into it later
She actually just got a new Nissan Rouge last week; she paid extra and got the premium package with nav and everything...she's almost at $250/month now, but at least she'll quit getting lost in the city
Speed