since this is a low milage vehicle I would also replace the front/rear diff fluids along with the transmission fluid /filter using the NEW DEXRON VI fluid.
the coolant should also be replaced now ....Dexcool gm approved coolant only.
the total coolant in this vehice is 4.25 gallons..you must make sure that you have at least 50% dexcool or the metal will corrode and gasket will blow out..
ALL 4X4 silverados have the locking rear differential. this is a mechanical locking diff. very reliable IF you replace the diff fluid by removing the inspection cover and cleaning out the gear box and magnet......
when it is slippery out I use the AUTO 4 wheel drive. with proper fluid replacement intervals of the drive train componets you should not feel this engage and drop out..
When in AUTO 4X4 the front axles are locked together so tires must always be worn at the same amount...never use tires of different sizes or wear..rotate tires every 15-20K miles.......