"Full Time" is called that because you can use it any time, even on dry pavement. That's possible because there's a "differential" between the front and rear output shafts in the transfer case, allowing the front and rear driveshafts to turn at slightly different speeds during turns.
"Part Time" is only used on soft or slippery surfaces, because it "locks" that center differential. The front and rear driveshafts have to turn at the same speed, so the tires MUST slip a bit during turns. This is not noticeable on soft ground, except during very tight turns, but it breaks axles and U-Joints on pavement! Incidentally, all Jeeps with the NP231 transfer case are restricted to four wheel drive use on soft ground because the 231 doesn't have the differential (the two driveshafts are always locked in four wheel drive).
Now, if you're getting stuck in "Full Time" but you get free in 4Lo, that might possibly be because the transfer case is allowing all of the power, through that center differential, to go to the spinning wheels (because they're easiest to turn if the rear end's on ice). 4Lo is "Part Time" though, locking that center differential, forcing the front and rear driveshafts to turn the same speed, so your front end can drag you off the ice.
So, go try it in "Part Time" and see if you have as much traction as 4Lo!