All sorts of combinations. My present equipment is reverse of yours ( Luch box front, LSD in rear), and most of the time I leave the machine in 2WD.
Driving with a "Automatic" locker is not something you take lightly IMO.
One needs to remember that when you let up off the gas, the locker un-locks and will re-lock after you apply power, but not before power is applied only to one wheel. This applies to manual, and automatic transmission equipped vehicles, but because of the on/off nature of manual shifting, the effect is much more pronounced on a manual. If you add to that the fact that in the Winter, the traction usually leaves something to be desired, you may have problems if you don't smooth out your driving habits.
I have a friend who has a TJ with a manual, who also lives in the mountains. His style of shifting is, well... let's say its rough. The vehicle is his DD and he lifted it and installed lunch-box automatic lockers front and rear. Well, it just about killed him. Not because the Jeep wouldn't go in the snow, it would, but because when the snow became more like ice on the twisty mountain roads, the torque effects of having one wheel engaged, then the other wheel engaged shortly after the up shift, made it a wild ride.
I added this to clarify the locker names that are being thrown around here:
Open a simple differental, when one wheel spins, the other is not delivered power.
Limited Slip or LSD a differental which always sends some power to both wheels regardless of the traction conditions.
Locker a differential which sends power equally to each wheel regardless of the traction conditions.
Lock-Right is lunch box locker made by Richmond Gear, and is sold under the brand name PowerTrax. When in coast mode, it releases the faster wheel. When you apply power, the differentail locks and sends power to both wheels.
PowerTrax also makes a No-Slip locker that is also a lunch box style locker that supposedly eliminated the ratchet/lock/unlock issues of the Lock-Right.
Aussie lockers are a lunch box locker made by Torq Masters, but are internally much like a Lock-Right.
Detroit is a locking differential made by Eaton. Eaton also makes Limited Slip differentials.
Truetrac is one of the Limited Slip differentals made by Eaton.
ELocker is a electrically selectable locker made by Eaton. When it is not locked, it acts like an open differental.
Trac-Lok is the OEM Dana Limited Slip differential.
ARB is a pneumatically selectable locker made by ARB. A compressor is required to engage the locker. Acts like an ELocker.