At 300 watts and a 100% efficient inverter, that's 25 amps from the battery. 500W is nearly 42A. What size heater do you want to run?

Of course, the inverter is not 100% efficient. Figure 85% and add that to what you need for two hours. A standard group 31 AGM battery should do the job just fine, and would probably run for more than one winter. This will cost you about $150. I do not know where to buy big inverters such as this, but boat shops should carry it (as well as the battery).

A set of smaller cells to provide 100V+ DC could power the heater directly. That seems like a lot of trouble, and a charging circuit would have to become creative, but it would be more efficient.