03 Prius

Lots of cars won't start when it's down around zero. Is it the 12v that's keeping it from starting? Low voltage? The battery may be frozen up. A battery warmer might help (I used to use a heating pad like you use for sore muscles.) Alternatively, get one of those booster battery things and give it a jumpstart.

Optima yellow top D51R is a proper replacement battery for first gen Pri's.

 

the original "moped" sized battery in the prius gen 1 is grossly insufficient to do the job that it is required (blower for heat and a/c, power windows, lights, radio, etc) and this battery is only charged when the gas motor is running. since the car frequently switches from electric to gas mode, when you turn off the vehicle when the 12v battery is not fully charged (happens often) and leave the car parked for a while (which is often), the battery will have a memory effect and it will never really achieve full charge status. it will slowly over months set a new peak charge point which gradually gets lower every time the battery sits without a full complete charge. Thus, in a year or two you will no longer have a battery that is usable.
My solution on my sons gen 1 (high school student also) is to put a full size car battery in the trunk and put it inside a plastic marine battery box that i bought at walmart. I connected the positive and negative terminals and wrapped the box very securely with a bungie and secured it to the hinge mechanism of the trunk lid so it does not topple. there is likely a better way to secure this but i haven't done it yet. i also put a 20w solar panel on the rear dash that fits perfectly between the two rear speakers. i connect a very small and cheap charge controller to the panel and then to the battery so the panel will continuously keep the battery fully charged.
A lot of people here will tell you that this is a bad idea as the hydrogen gas that is emitted from the battery while charging needs to be vented or the car will blow up. Its been almost 2 years and the car has not blown up yet. I also live in missouri (st. louis). I asked a prius mechanic what he thought about my mod and he said not to worry about it. there will never be enough hydrogen gas accumulating in the trunk to blow up the car. If you are worried about it, remove the vent hose from the original battery enclosure and figure out a way to connect it to the marine battery box.
This mod has fixed all my starting problems and its been 2 years of very reliable service. I love this car and if my son ever gets rid of it, i will happily take it from him and keep it as my own.

 

Interesting, John, two years ago I went just the opposite direction. I got a small sealed UPS (like a mobility scooter) battery and patched it in. It fits fine, is even smaller than the Prius battery and hasn't given me any trouble. Every time I take my Prius out, the battery gets charged. I believe that you are incorrect about what the little 12v battery powers. It mostly serves to keep the computer settings and turn on the various relays before you start the car. After you start the car, the HV systems provide 12v power.