The blower motors are pretty power hungry, on the order of about 330 watts, give or take. For a 12V system that is about 30 amps, or about 2 hours of output from a typical deep cycle batter before you risk depleting it to the point of damage. An ~$300 12V Lifepo4 battery might get you 4 hours of runtime, but not much more than that. In most cases, an outage of less than 8 hours won't get things so cold in a decently insulated house that you need to worry about it, and IME, an outage that lasts more than 8 hours has high probability of lasting much much longer.
TL;DR - Your deep cycle battery approach may not prove to actually be worthwhile, consider working out the car-as-generator hookup plan in advance.