Trickle charging in cold

I would only recommend you replace that 12v battery every 5 years so you won't run into it dying in the cold winter months. So check the date, if it's over 5 years old, get another one and you won't have to worry about trickle charging

 

I say couldn’t hurt. Make sure you have a charger that works with AGM batteries. It doesn’t need to be super powerful either. Max charge on a 2nd gen Prius is under 4 amps.

 

welcome!
hybrid battery is fine.

in your shoes, i would poly use a maintainer just in case you don't drive it for awhile. it really depends on the 12v battery age, condition and usage. but it is a weak spot in the prius.

you may also want to consider a block heater, and remember, the jump point for the 12v is in the fuse box under the hood

 

I would keep a 12 volt battery tender on it if hardly driven at all like your doing. Short trips only are hard on everything in a Prius especially the 12 volt battery. 10 miles in the winter is hardly even warming the car up.
Plus that’s really hard on the hybrid battery.

Get a good quality voltmeter and get acquainted with measuring the dc battery voltage at the front jump points to keep an eye on it you do not want to be stranded with a dead 12 volt hilarity sometimes happens to your wallet there.

Never attach anything directly to the battery in the trunk, use the front underhood jump point only.
That’s what it’s there for.

If hardly driven like your doing in the winter I would once in a while put the car in inspection mode and let the engine run for A while. Use high quality engine oil.

Go on YouTube search PRIUS INSPECTION it will give you the steps to put the car in inspection mode lets the engine runs endlessly.

Bottom line a G2 Prius does not do well with short drive life. Car needs to run long enough to charge both battery’s.

And lastly hardly ever using the ac is death for that system. Try to run the ac once in a while in the winter.