Hi Chas,
Sounds like the Cherokee has Jeep's Command-Trac 4x4 system. The part-time light means that the 4x4 system is engaged, but you only want to use the part-time system on slippery surfaces. You'll notice that if you have this system engaged and try to turn corners, you'll get tire scrubbing, skidding, or a bouncing motion from your front tires. This is because this 4x4 system locks all four wheels into turning at the same rate, and the inside tires need to turn at a lower rate than the outside ones in a turn. If you're in snow or mud, you probably wouldn't notice this issue (and it won't cause damage) because the system can handle the tire scrubbing better on a slippery surface. On dry pavement, this could cause damage to the hubs, axles, or transfer case.
Other versions of Jeep's 4x4 systems (such as Selec-Trac or Quadra-Trac) will have a "full time" mode where you can run it on dry pavement because there's a differential that allows the wheels to turn at different speeds.
Only use 4-Lo offroad or if you're stuck in snow or mud. Your max speed should be about 20-25 miles an hour in this mode due to the lower gearing. Never use this mode on pavement. You may find that it's easier to shift into 4-Lo if you're moving slowly, like 1-3 MPH.
Finally, you may want to check out the message boards at
http://www.jeepsunlimited.com/ -another place I hang out sometimes to learn about my Jeep.
Good luck!
Todd
