Duallys are not good in the snow as it is cause the back wheels float more then a single rear wheel..
Do you have shift on the fly or the buttons on the dash?
Your rear may not be a locker either. And the front on those trucks are never a locker.
If the front was not engaging there could be a few issues..
They work by vacuum and electrically on some.
If you have shift on fly this engages the transfer case. If the buttons then a electric motor with a worm gear engages the transfer case. These work gears strip if you have that type.
Then once engaged there is a vacuum switch that sends vacuum to a actuator thats usually under the battery box. This in turn pulls a cable that goes to the front differential. This engages a fork that locks one wheel only on the front.
$ wheel drive on most trucks with open rears mean 2 wheel drive. One front and one rear.
Now if you have a locking rear then its 3 wheel drive.
My advice would be find out what rear you have. If not a locker, then get one there.
Then fix what issue you may have with the front..
Mike L ... N.J.
2006 Silverado ext cab long bed. 3:42 rear. LM7 5.3 motor. 300 hp 350 ft lbs torgue @ 4000 rpms
2018 coachmen Catalina sbx 261bh