You are asking two different questions. The trailer is 110vac, and of course the A/C will run off 110vac.
Now, you say you don't have the time to run a 30 amp, 110vac line to the trailer? If the current service is a 15 amp circuit, it *might* run the A/C and it might not depending on the start surge that your unit requires. A 20 amp circuit will most likely run the A/C with no problems, but don't try to run the microwave or mama's hair dryer at the same time.
If all you have is a 15 amp circuit, running the A/C is not advisable.
As for the extension cord, the trailer draws what the trailer draws. If you use too small an extension cord, you are pretty much guaranteed problems, especially if the cord has a lower rating than the circuit.
Distance matters. On a 15 amp circuit you'd be asking for trouble on a long run out to the TT with a under capacity cord and then trying to run the A/C.
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