Scott,
As NMuzj said, the locking of the center will keep all power from going to a single wheel. While 4WD vehicles indeed deliver power to all 4, their achilles heel is allowing the single wheel without traction to continue to spin. There are two major types of controls that prevent this: mechanical and electronic. Mechanical controls - such as front, center, or rear locking differentials (aka 'lockers') make the locked channel operate as one piece. In the case of the center lock, it will force a 50/50 power distribution between front and rear. This means that at all times at least two wheels will be spinning. If you have a rear locker, then (if locked) a minimum of three will be spinning. So coming back to your question, the center lock is used to maximize available traction on slippery surfaces.
Later LC/LX's use electronic traction control in addition to the center lock (and they lose the optional rear lock). In this paradigm, the ABS system is used to brake undesirable wheel spin, therefore channeling power to the wheels with traction. The same system is also used to provide vehicle stability control by using differential braking to keep the truck from undesirable spins or rolls.
For your mountain trip, tires will make the biggest difference in your success than anything. A good snow (or even mud+snow) tire will maintain traction longer. Also remember, that good tires also improve braking.