To be clear though, as the OP was asking about LSD's - LSD's like the TruTrac is awesome up front in snow/ice conditions, and should not be confused with auto lockers (although it's a common mistake).
The TruTrac is "auto", but not a true locker.
It is my belief that in snow/ice driving, a TruTrac is better than an open diff as well as locked axles. Technically, if you are stuck, a locker could be better, but when the trail involves turning or off-camber, I'll personally take the TruTrac over a selectable locker. So much nicer for emergency maneuvers in the city too during a winter storm.
I have TruTrac's in both my front and rear and love them.
It's my daily (only) driver and I see more than my fair share of snow/ice conditions, which influenced my decision heavily.
So far, I have never gotten stuck or unable to complete an obstacle my Jeep group does, which includes a couple mud spots that locked Rubicons got stuck on. (weight, tuck, tires, driver, luck, etc, can also factor in that).
*note: there were some very steep rock climbs I bypassed that the the 4-door Rubicons did.
1 locked TJ also did it, but nearly flipped.
So essentially the TruTrac's have never failed me on anything I was brave enough to attempt. Key word being "brave", lol.
If I lived in a place with little to no snow however, I would put some serious thought into a selectable locker - but I am very pleased with my choice of TruTracs. I think a lot will depend on your expected use of extreme rock crawling vs other types of driving.