The alternator on my 1993 f150 4.9L engines has small gauge wiring plugged into it. If the alternator furnishes electric current while the engine is running, how can the alternator wiring (looks like #14) be capable of furnishing power to large current components like an air conditioner, electric defrost, etc.?

 

There is, should be, a 10 gauge wire located on the back of the alternator that connects directly to the battery positive.
Keep in mind today's alternators are not intended to be battery chargers , but to only replenish what the vehicle took from the battery to get started or supply what the vehicle requires while running (all accessories). Trying to charge a very low battery can overload the wiring from the alt to the battery.