In Germany, cars are required to be equipped with a specifically spec'ed first aid kit.
You could use that as an orientation.
Also, gloves are a good addition, and a thermo-foil-blanket (in case of burns, car getting stuck in the snow). Scissors are convenient too, and possibly pincers. If you want to go fancy, there's resuscitation masks. A seat belt cutter can also be useful.
If you have the space, you might want to add a woolen blanket, which can help to extinguish people, or even carry more heavily injured parties.
The only thing, that could possibly be impacted by the thermal stress, that an outside environment poses, is an antiseptic.
You could also add a booklet of lifesaving measures (pictograms?) to your pack, so that there is a guide on how to get someone onto their side, how to treat a shock, or how to tie off a heavily bleeding wound.
Some plastic bags can also be helpful, to collect severed limbs.