How fast can you drive in 4WD or AWD?
In general, as fast as you want.
However, your local laws have a word in that as well. Not only the posted speed limit will need to be observed - depending on the weather conditions the law might might keep you from even getting to the speed limit. In many states you will be fined if you go too fast for the road conditions (could include anything from rain to ice).
It will be wise to not only to eyeball the law - you are responsible for your own safety and should slow down when the roadway gets slippery (a fine layer of sand spilled off a truck could make asphalt very slippery).
4WD and AWD makes driving on lower traction surfaces more stable and a bit safer. But neither 4WD nor AWD plus their added stability features, like traction control and stability control, can defy the laws of physics. If you are too fast - you are too fast. Even if you were going very slow on snow and slipped off the road - you were simply going too fast (for the present conditions).
The best safety feature of every car is still the driver
. Be safe! Be Careful! Slow down!
Back to the original question - "How fast can I drive in 4WD?". As fast as you like - none of the 4WD or AWD systems has any mechanical speed limitations. Speed will do no harm to the drive components.
There is one exception though. Owners of part time 4WD systems (the ones that let you chose between 2WD and 4WD) should be very cautious when using 4WD on slippery roads, because their handling is not as precise as full time 4WD and AWD.
For one, they should always shift back to 2WD when approaching dry surfaces (and back to 4WD on slippery stuff) because part time 4WD should never be used on dry surfaces. If you do, you can cause severe mechanical damage.
Also, when in part time 4WD neither ABS, traction control or stability control will work.
The faster you (accidentally) drive on hard surfaces in part time 4WD, the more likely it is that mechanical damage will occur. Here is why...