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A small LFP battery can still work fine in the winter, the problem is you need to have a method of warming the battery so it can accept a charge. LFP is still more economical if you're willing to deal with a heater (a quick and dirty way to get it done is to have a heater pad that consumes enough power that an idle engine doesn't produce enough extra amps to charge the battery, and switch it on immediately after cranking).
I was talking to a manufacturer who can provide 40Ah LTO batteries (which can charge in the cold) in a plastic case with SAE terminals, but the cost is fairly high; The final cost if I were to resell them would be around $500. This would be a true no-compromise lead acid replacement that lasts forever, has ample reserve capacity, and has great cranking capacity. I've been thinking about starting a business selling these to luxury sports car owners, since they pay well over that amount for LFP batteries.
You can get a smaller LTO battery with no BMS for less money, and just run it with a balancing circuit. Used cells (which retain most of their performance since the LTO chemistry is more durable) should be able to get you around 20Ah for under 100 bucks total.
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