If a 4x4 (true 4x4 not AWD) has 3 wheels slipping, does the one tire with traction receive all the torque available from the transmission? Is there typically a reduction in power transmission in 4x4 systems to the wheels that are not normally powered (i.e. front wheels on a pickup)?
It depends on what type of differential it has.
The nature of an open differential (as found on normal road cars) is that the spinning wheel(s) will get all of the torque.
Proper off-road vehicles will usually have a diff-lock selector which works on some of all of the differentials which means that both driveshafts the diff is connected to get the same torque, regardless of slip. This should only be used at low speeds on slippery surfaces as the locked differential won't be doing its normal job anymore.
More sophisticated vehicles may have limited slip differentials which are a compromise between an locked and open differential and in some cases allow adjustment of the degree of slip either by manual selection of computer control. Depending on the degree of slip selected the differential will always send some fraction of torque to both wheels regardless of their relative speeds.
Limited slip differentials are particular useful on vehicles which are intended to drive at speed on loose surfaces eg in rallying and for permanent AWD cars as they can also be used to adjust turn-in characteristics.
Another option is traction control which monitors the relative speed of the driven wheels and applies the brakes to lock the spinning wheel which transfers torque to the opposite wheel. The are also manual versions of this known as 'fiddle brakes' where the driver has separate brake levers for each side of the vehicle (or front/rear) this system can also be used for 'skid steer' a bit like the way that most tracked vehicles are steered.
Only if the differential is limited slip.
If there is no limited slip diff then the wheels with no traction will just spin wildly and no torque is transferred to the wheel with traction.
Some off-road vehicles let you lock the diffs so that torque can be delivered to all wheels regardless of traction.