Subaru and trucks aside, most AWD systems are 'slip and grip'. The vehicles are powered through the front wheels 90% of the time. Once the computer senses that the front wheels are slipping (like when accelerating away from a stoplight or stop sign) then it will direct some of the engine's torque (up to 50%, usually less) to the rear wheels, to help the vehicle accelerate faster. This process happens within a few milliseconds, usually.
The problem with such systems is in deep snow. If the vehicle is stuck, or about to get stuck, that few milliseconds that it takes for the computer to shift power to the rear wheels can make the difference between getting unstuck or getting out and digging/pushing. This is why Fobroader mentioned the 'center differential Lock'. I believe vehicles like the Mitsubishi Outlander and Nissan Rogue (among others) have such a device. When you have this device activated, it will send a certain percentage of torque to the rear wheels (between 30% and 50%) all the time, up to a certain speeds (usually around 40-50kph) at which point it reverts back to normal 'slip and grip' mode. This permanent split of torque makes an AWD vehicle a lot less likely to get stuck, and a lot more likely to become unstuck when travelling through deep snow (think unplowed residential street, driveway or parking lot), especially at intersections where the windrows and ruts build up.
As mentioned before, Subaru's are different. Their AWD is on all the time, so power is always being sent to the front and rear wheels. The downside to this is slightly worse fuel economy, but in recent years even that difference has gotten noticeably smaller. Subaru's have their own set of problems, however, with decidedly low-rent interiors and questionable engine reliability (although our resident Subie slappie will come on here and tell you that no, the interior on his $40 000 top of the line Forester XT is quite nice, and that the head gasket issues are blown waaay out of proportion).
Once you get into higher end luxury vehicles, as well as sporty cars, things get even more complicated, with AWD being used not only for wintry conditions, but also to improve handling and performance, with such things as torque vectoring.
EDIT: I may be wrong. The Nissan Rogue may not offer a center diff lock anymore. Certainly a vehicle like the Cherokee would.