If you’re only using half the capacity of the inverter, then #4 wire is fine, but a bit small if running it to its capacity.
In mild weather like +20 F like you were camping in, your lifepo4 will work fine if you keep it “warm” through use/load. At least my bike battery does. But yes they’re a poor choice in general for cold conditions.
Biggest issue is you have a very expensive battery and not much reserve capacity compared to the $ invested. And only 100ah doesn’t really cut it if you’re actually using more than nominal power usage. But buying another one is another $900 expense and you still only have “average” reserve capacity.
Why not just run your genset in conditions like this? That is the actual easy solution for occasional use. It solves all your problem with no additional expense or effort.
