I used to be an avid off roader and winter snow driving was what I enjoyed most. When driving in reverse, there is essentially no techology that is going to keep you from sliding. The only thing that could help would be a very low gear, but you won't have that option in reverse,
I would recommend backing your vehicle into the garage if you knew snow was coming. Then use the hill descent control option, which I beleive the ST's have, and then your lowest gear, to slowly "walk" your explorer down the driveway.
You will have more control and coordination in operating the vehicle by driving forward instead of reverse, especially in the above settings.
Also light snow will often casue more problems backing down than heavy snow. Heavy, deep snow, will provide a some resistance and as you slide it will build up as you slide adding a little more resistance and that helps. So I would expect you to slide more on thinner layer so snow in contrast to very heavy snow. And depending on wet vs dry snow and whether some of the precipitation has a frozen layer under the snow will change how your explorer traverses your incline.
One snow storm you may have some control and another you may slide much more. All depends on the type and depth of snow.
Snow tires are not going to mitigate much, if any at all, of you sliding in reverse. They will provide much benefit on forward motion and some stability from sliding laterally, but not much of anything in reverse unless you were trying to accelerate, which you won't be doing on an incline.
I use to have a jeep wrangler with a highly modified suspension and very deep treaded mud tires. And I could power through very diffcult sections of snow. But on a hill in reverse, I would often slide significantly.
