Reason when going in a straight line both rear wheels are turning at the same speed. Because both wheels are covering the same distance at the same speed.
When turning the outside wheel has to cover more distance then the inside wheel. Open rear differential (clue as to why it's called a differential) is that when making turns the wheels have to be able to turn/revolve at different speeds. Other wise the tire that does not keep up with the axle will be dragged forward by the axle to keep up with the other wheel. Tires resist being dragged on pavement.
Limited slip rears will let the wheels turn at different speed when turning, acting as an open rear. Then will not let the wheels slip so both wheels get power when going straight because both wheels are turning at the same speed.
When tires start to lose traction the limited slip mechanism will try to keep the rear acting as if it was a locked rear and both wheels get power. However if enough gas is given the limited slip mechancism will allow rear to act as an open diff then all power goes to one wheel. One wheel spins and you go no where.
This is why limited slip is no where as good as 4wd. Though a lot better then an open differential.
Permanent locked rear. When on dirt and the rear is locked so both wheels have to turn at a different speed the slower outside wheel/tire will slip in the dirt easily as it is being dragged to keep up with the faster moving inside wheel/tire. When going straight or turning and you open throttle wide both wheels will always get power no matter what.
Jeeps and I sure there are others that have locked/lockers differentials that can be turned off an act as an open diff when on the road and can be locked by the flip of a switch for when off road. Jeep has front and rear lockers that can be turned on and off.
Yes you can drive on a snow covered road with the diff's locked because the tires will be able to be break traction enough with the snow to get dragged when the tires are being turned at different speeds.
However plowing with a locked rear is not good because the trucks wheels are behind the plow on pavement that has had the snow removed.