Cold weather finds bad batteries. I have chased these issues for 45 years in my business. Yes even 40 degrees can sort out bad batteries.
I could always tell when we were going to get a batch of customers complaining of dead batteries or "shorts".
However you must first check the charging voltage. With the engine running it should NOT go dead. You should see 13.5 when idling and a bit more is fine.
IF you have that voltage with it idling then replace the batteries. If they are over a year old just replace them.
We do NOT buy batteries. We just rent them and they can fail in a day or years but generally a couple of years on starting batteries.
You can scratch your head and have them "load tested" etc but why the heck waste time if the Alternator is working.
I sent a fire chief out three times telling him his brand new vehicle had a bad battery. It was just a few months old. His mechanic said our radios "had a 12 volt draw". Of course there are all kinds of tiny draws but a dead battery while running or after two hours is not a sign of a short. If there was a short (which is incredibly rare), something gets hot.
The fire chiefs mechanic would not change out the "new battery" so I just bought a new one and put in in place. Asked the Chief in a few days if his problem was solved. I then sent him the bill for the new battery with the invoice for what it cost.
Of course your cables must be in proper condition.