"THe guy who jumped my battery recommended not driving it but leaving it running for at least 30 min with everything turned off. So yeah he could have sat in his car for that long without heat but since the cold is probably what drained the battery that would be harsh. But that is still not stranded for the night. just for an hour or so."
That's far longer than a battery that was just cold would need to be reasonably operable, and I've never encountered anyone who ever recommended idling a car for half an hour just to charge the battery. I agree that the alternator won't charge the battery as quickly while driving the car as it will in idle, but still a drive will do the job unless the battery is damaged (in which case it probably won't hold a charge no matter how long you run the car) or in very deep discharge, in which case a half hour probably wouldn't be enough to fully charge it anyway and he'd need a booster jump to get it started the next time he wanted to drive. In either case, once the car is running, there's no need to idle it to recharge right on the spot. If your car can't run normally once it's started without a charged battery (and in fact, with no battery at all), then your alternator is broken and needs to be replaced but you'll find that out when the car stalls the moment the jumper cables are disconnected.
As a side note, cold doesn't drain a battery (besides a small percentage of the charge due to thermal differential). It just makes it so that the battery doesn't discharge as efficiently, so the power it can provide drops. I compare it to a gallon of water, where the water is the charge. Fill the bottle, and you can pour off a gallon before you need to refill it. Freeze it, and the bottle is "dead" because no matter how you tip it, no water comes out. But heat it back up, and it goes back to working. For this case, if the battery is on the edge of failing such that freezing it causes failure (rather than the failure being due to discharge like would happen if he left his headlights on for more than a day), it'll go back to working as well as a failing battery can when the engine warms it up.
Still, for the purposes of this thread, the important part is that he was only "stuck" until Calistoga's DH arrived and jump started his engine. After that, he could have gone anywhere because he wouldn't have to sit with the car where it was, he could have driven it and then idled it when he arrived, and having gone to Calistoga's place, he could have left even if he needed another jump start to do so. Because of that, he wasn't prevented from leaving so he can't plead "captive guest" in terms of them giving him more leeway.
"If you turn the engine off then it isn't going to recharge."
I think you misread her modifier. I don't think she meant "turn it off to recharge", I think she meant run for 5-10 minutes to recharge before turning it off. I agree with you that that could be too short, though, since I usually suggest fifteen minutes at least.