A 12 volt battery would run a 1500 watt heater for around 24 minutes to 5 minutes depending on the amp hour of the battery. Adding more than one 12 volt battery will allow the 1500 watt heater to run for 1 hour to around 84 minutes.
1500 watts are a lot of watts and will drain batteries really quick so it's not ideal to run 1500 watt or any other electric heaters on 12 volt batteries or solar systems.
Instead a good portable generator will work better but if you can use propane to heat with then that would be cheaper and warmer.
The best portable power station is the Jackery Solar Generator Kit 4000 and It has a 3000-watt output which is enough to power most devices.
Other good portable power stations are.
Jackery Explorer 2000 Plus.
BougeRV Flash300·
Jackery Explorer 1000 Plus·
Anker Solix F3800·
Bluetti power station.
A portable power station has a battery that is rechargeable either by solar panels or through a vehicles 12 volt outlet or when you plug it into the house.
Once the battery of the portable power station is charged it will provide you with 110 volt electrical power through the regular electrical outlets.
The battery powered outlet is basically a battery with an inverter built in that converts the 12 volts of the battery into 110 volts to power 110 volt appliances and devices.
However the portable power station will only provide 110 volt power for as long as the battery stays charged but using a solar panel to keep the battery charging can help keep the 110 volts flowing.
You can also setup solar panels on other batteries and use an external 110 volt or even 220 volt inverter to get regular electrical power.
Another option is to use an inverter in your vehicle and while your vehicle is running it will provide electrical power through a 110 volt outlet.
After you shut the vehicle off though you should unplug the inverter or turn the inverter off so it doesn't draw your battery down.