I took the car to a local auto parts store and they put a tester on the battery. The vehicle was running and the tester showed both batter and alternator were OK. That's all that was done in terms of that.
Good suggestions though. It's probably due for a tune-up anyway, so I might as well get at the plugs and wires, going the extra mile and doing the coil too. And as far as I know, it has the original battery (50K), so I could try your suggestion Blurvfocus and get another.
It does only seem to do this when it's relatively cold out. It started when it was in the teens below zero, but most recently acted up when it was in the teens above. So I'm not sure what temperature has to do with it, as this is the first winter we've had the car.
Thank you for your suggestions.