For traction on the hills, weight is paramount. Any of the Deere 300, 500, or 700 series machines would fit your need. I'm sure there are Kubotas, MFs, and NHs that would work too. Also consider Simplicity or a ZTR.
Or think about buying a used Deere, like a 425, 445, or 455. These machines are awesome and will last a lifetime. They are certainly heavy enough for those hills. I mow a 20 degree slope sideways with my 425 AWS with no problems slipping or fear of turning over. I have pushed snow as deep as 25 inches too (with chains and weights). Mine is on its 13th season and still looks and runs like new. I recently saw a 445 with 60" mower and power front blade with 600 hours on it for $3500. I thought the guy was giving it away, at that price. If you can find one for less than $5K in good condition, you can't go wrong.
A Gravely tractor (not walk behind) is also good and heavy, and well made. Many have the engine mounted directly to the rear axle, very low to the ground. I owned an old one, and it couldn't be stopped and never slipped. With just 10 hp, it actually gave a better cut than my Deere.