Just trying to be helpful. A lot of TV/cable amps also run on 12VDC, I know the ones I use on my OTA system do. I'm not using a preamp on any of my scanners, pretty good coverage on the statewide TSYS here. I have a Pro-197, a WS-1095, and a WS-1098 at home, I actually piggybacked all 3 mobile cables into one lighter plug and when my power goes off I can run all three from a HFT jumper pack for many hours. The point I'm making with all of this is that the load isn't a large one. You could easily piggyback onto a power port, either with a plug or going direct to the wiring, and all would most likely be fine. And many vehicles de-power these ports when the key is off so that solves the battery drain problem. Of course using an inverter, you need a way to de-power that as well, as they will draw current whether you are using them or not. I've been down that road too, both with my own vehicles and eliminating generators on fire apparatus. Vehicular installs can be a lot of fun.
Very much agree in re the cold weather!