There are all sorts of trade offs in electrical systems. Basically power to do a given task is the same in watts. In electricity, Power is volts x amps (at least when you are talking DC) so if you are running a 9 watt LED it is going to draw about 3/4 amp. Any time you have to run a converter/inverter to change voltage or change from DC to AC or vice versa, you are going to lose energy. There should be an efficiency rating for a converter if you can find it. 80 - 85% is pretty good. In other words, you lose 15 - 20% in the conversion.
There are also losses in the distribution. A wire has resistance and conducting electricity causes it to heat up. The heating is proportional to the current so less current at higher voltage will deliver the same amount of power with less loss. That is why a 24 or 48 volt system might be a little more efficient but everything has to be capable of running at the same voltage.
Most of this stuff has been used in RVs for years so you can get some ideas there. Incidentally, there are RV televisions if you want to save a little more energy.
https://www.amazon.com/Free-Signal-TV-Transit-Powered/dp/B07CBSGR5F/ref=sr_1_4Claims 49W so about 4 amps at 12VDC.
Modern TVs run on low voltage DC internally so they have power supplies that convert 120VAC to low voltage DC.
The idea about putting the batteries in a root cellar is valid. If you can put them deep enough in the ground, they won't freeze even if they get run down. Running them too low is hard on a lead acid battery, but freezing is usually a killer.
Some things make sense in different seasons. For example gas lights. Horrible in the summer when the solar cells and LEDs work well, but provide some needed heat in the winter when the solar cells are weak.
It will take some time and experimentation to come up with the best solutions for your needs.
Jerry