The Honda HR-V is essentially a Fit with a raised suspension and optional AWD, but it's too new to be available for $15k.
The Honda CR-V isn't special in any way except that it's very reliable. Same for the Toyota RAV4, which has been very reliable except for the 2006 (first model year of that generation).
The Soul has been very reliable so far in our survey, but the oldest ones are 2010s. Plus you can't get them with AWD.
The Mazda CX-5 looks reliable so far, but the oldest ones are 2013s.
But these are probably all larger than you need. Reliable compact hatchbacks offered with AWD include the Toyota Matrix, Pontiac Vibe, and Suzuki SX4.
Be sware that AWD only helps you get going. For safe braking and cornering winter tires provide far more benefit than AWD. Even fitting your Fit with winter tires might be a solution.