turning off DSC has nothing to do with affecting the AWD system xDrive. Normally DSC works with xDrive (they're two seperate things) to keep driving safe. Like someone mentioned, xDrive is never shut off and the X3 remains a variable-AWD unless there's a failure in the system, in which case the X3 defaults to rear drive.

Pressing the DSC button shuts DSC off but retains DTC (Dynamic Traction Control), which has a higher threshold of intervention so you can move in deep snow, dirt, gravel...etc. Holding the DSC button for 3 secs shuts off DSC and DTC, but xDrive itself is unaffected.