If the heater is the typical 1500 watts that’s 12.5 amps out of your 20. I’ve done it (and 15a) many times, albeit sans heater at 15. So be careful what else is on… keep the fridge on gas and watch the lighting, TV, etc. Start with fully charged batteries so the inverter’s charger isn’t maxing out while the heater is on. If you have diesel hydronics use that for heat when possible. Also note that a long 14 gauge cord will drop some voltage, so keep that short (25’) or use a yellow 12 gauge.
Joel