I had an early ranger bought new back in the early 80's with front and rear LS. I lived in the Wash DC area and I drove it through snow and ice without any of the problems described here. Stock and with a suspension lift and big tires. Wheeled it offroad a lot. We lived off a long downhill road that had a good crown in it. I pulled lots of cars out of the ditch on that road with that Ranger. Seems that most people never learn that with the brakes on you can't steer on ice.
My current BII I have has a factory LS in the rear only. Memphis doesn't get much snow but gets lots of iced over roads. It's got P235/75/15 snow rated General Grabber AT2's and I haven't needed 4wd. 4wd makes driving much easier on the steep hills but unless I try to get stuck 2wd gets the job done.
Back then my parents had an 86 BII with open diffs and it was good in the snow but it stayed home in the really bad stuff and I went out in the Ranger. I had that 86 for a few years and couple of Dallas ice storms and it did ok but it was a long ways from what my current BII can do.
I will admit that it could be that biggest difference is the tires and not the LS diff. Those OEM Goodyear Wranglers that Ford loved to install weren't the default tire because they were a great tire
But in the end, IMHO, a LS diff is worth it and every truck I bought new had it optioned until traction control came along and then I optioned a selectable locker over a LS. That was a 2013 F150 2wd and there were times on the ice here where that F150 wouldn't get going in TC alone and it took the locker to get moving.
(Sidetrack rambling...) it was that F150 that trailered my BII home from Dallas when I bought it because I thought it was nuts risking the F150 on the ice and I needed a "beater" instead. LOL, my "beater" has a ton of money sunk into it now.