Lead acid battery cutoff voltage circuit
There are voltage monitor ICs, which perform this (or similar) functions, intended to disable (by logic signal) a circuit when voltage is low.  This one LT2965
seems suitable for your needs.  It works by detecting low voltage, and requires that your device take a logic signal input and cease consuming power.   There is a small current drain (at 12V, something under 10 uA), but most batteries can handle that for a year or two.

A 'turn-off' threshold should be set according to the lowest charge state at
the (coldest, if I understand lead-acid batteries) temperature.  The
'turn-on' threshold should be slightly higher, so that diurnal temperature
variations don't cause it to toggle.