Why would you need a second hose to pull air into the unit to cool the compressor? Will air not be pulled in through the side grills?...
Well, it's not the compressor which needs cooling, but the condensor coil, but the idea is the same - some source of air is needed to dump the heat into. If there is not an intake hose for that air, it will be taken from inside the trailer, and that will be replaced by more hot and humid air from outside through whatever path is available. The better plan is to pull outside air over the condenser, and send it back outside again.
The inside and outside air paths are normally quite separate in any air conditioner, except
these one-hose portables; inside air goes over the evaporator to get cool, outside air goes over the condenser to pick up heat. Most people don't have central air conditioning
in their house, but do in their car, so I'll use that for illustration - the A/C condenser in a car is that extra radiator ahead of the engine radiator, fed outside air and not exposed to the air inside, while the evaporator is in the heater/fan setup under the dash (along with the heater core), absorbing heat to keep the inside air cool. For another example, in-window units draw air from the outside for the condensor, which is properly considered and nicely shown in Steven's original post to start this topic.