Pixguy, you might be surprised at how well turfs work on snow. I used to keep the BH on for increased traction --and it works very well for that-- but I also have a steep driveway and found the front end would float on the way uphill. Steering was almost non-existent; the tractor just followed the contours of the driveway crown, whichever side I happened to be on. Made for a lot of mid-slope "aiming adjustments" on the way up!
I left the BH off last winter as a trial, and found I could go uphill and still control it. It did make me use 4WD more for traction, but hey-- that's what it's for. In any case, it worked well (and was certainly more maneuverable, being several feet shorter in the rear!).
How steep? It a couple of sections, my driveway hits 12-15 degrees of slope. I also have "plain" (unfilled) tires, and chains, though I've never used them... yet. WBB