The tube is a  water vent tube, it allows you to do things like drive
through water without getting water into the transfercase.  Depending
on how long the tube is (and the other vent tubes are) you will get an
idea of how deep of water you can drive through.  My guess is nothing
more the puddles.  I have vener seen a Bravada actually go off road.
If there is oil coming out of the tube then water has gotten into the
t-case and is forcing the oil out.  The t-case needs to have an oil
change.  Make sure you use the oil the GM recomends.

Snow