We use an electric heater with a blower to supplement the gas furnace. 1500 watts ain't much heat but is a lot of electricity. We have one with a thermostat (and remote control) and another use is to keep the cabin above freezing in the fall and spring when the trailer isn't winterized. But it takes 120vAC power, not 12vDC.
1500 watts at 120 volts is 15 amps, half the trailer's electrical capacity. Thru an inverter at 12v that would be 150 amps (watts is watts) in a perfect-conversion world (that doesn't exist). You'll drain the trailer battery in a matter of minutes -- maybe 5 before the inverter shuts down from low voltage. Takes cable, not wire to handle that many amps. I tried running a simple hair dryer off a pair of Trojan T125 batteries and everything shut down in about 15 minutes.
With all the AC outlets in our Roo on the same 15a circuit my wife's hair dryer will trip the breaker if the space heater is on. Always surprises her!
-- Chuck