The NP231 can be used on slick or loose surfaces only, no dry pavement. You'll often hear the 231 referred to as a "part time" T-case, that's because it is only designed for part time use on loose surfaces.
The 231 locks the front to the rear and has no provision to decouple irregularities in the two drivelines, that's why it requires "loose" surfaces because it uses the driving surface to decouple the driveline differences.
Driveline differences can be caused by tire irregularities or especially when turning due to one wheel turning faster than the other due to differential effect. You'll notice that when you are turning in 4wd you'll feel the tires scrubbing.
You could probably "test" a 231 on dry pavement in a straight line for a short distance to make sure it works, i.e. like when buying a used vehicle and no loose surface available nearby.
Driving with it in 4hi on snow and ice is no problem. Even though ice is so slick I noticed that it does help stabilize you and make the truck feel more surefooted, you'll still slide just not as much. I used to have an '88 GMC S15 Jimmy with a np231 and it rocked in the snow. (used to live near Chicago).
HTH,
Mark