NO! A typical A/C unit draws at least 15amps at 110VAC, 1650 watts. A high end single car battery can supply 80amps at 12VDC or 960 watts for about 1 hour. Battery would be dead in well under an hour. Now add in the loss of energy going thru a 12vdc to 110vac inverter and its even less.
What you need is a 3000amp generator such as a Honda or Yamaha. Then you could easily run your trailers lights and A/C for hours.