It really depends a lot on the snow. Lately --over the last several years-- we've had a bunch of wet snow or snow/rain combination events. In those cases, the snow can quickly be compacted and become like ice or grease -- extremely slippery.
If I haven't yet put my rear chains on, there've been times when I'd lift the blower up some (or all the way in extreme cases), claw my way up to the top of the driveway, and clear snow with the blower
only on the way down. I don't believe the float has much to do with it, it's just the lack of weight on the front and the steepness of the slope. (I've threatened to add a couple hundred pounds to the top of the blower on occasion....)
I had thought, years ago, about chains on the front, but that really won't help with the weight issue -- and the chains I got, that were supposed to fit my fronts, were way too big and I haven't ever tried to modify them to fit. After I removed the BH, however, it got better.
Incidentally, the same thing used to happen wth my walk-behind blower. It was 24" Toro with a weight-shift mechanism (rocked the drive wheels to the rear about 6"); I had to use that wheels-shifted-to-the-rear position
every time I went uphill, to keep the blower scraper from lifting up. (After 18 years of that, I got my 2310!)
