There’s so much grey area in battery technology that it pays not to think in black and white terms.
Attached is an article comparing the effect of cold weather on AGM versus lithium batteries. While the comparison seems highly biased to make lithium look that much better, it does touch on the limitations of lead-based batteries when used in cold weather. And more importantly, how a fast discharge rate reduces AGM total energy capacity.
The comparison only goes to 80 Amps with 210 Amp-hours of battery capacity, which means about 1,000 Watts from two large group 31 deep-cycle AGM batteries. Even that drains them fast, and you’d need twice that (about 2,000 Watts) to power a microwave.
Ignoring the lithium data altogether, there’s much to consider regarding AGM batteries in cold weather and or fast discharge rates. Test is a little flawed and biased, but worth looking at in my opinion.
https://battlebornbatteries.com/lead...e-paper-study/