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Is your battery near the end of its service life? batteries are rated for 48 mos, 60mos,etc. Cold weather is hard on them and if they are getting weak it will show up when it turns cold.-Jack
Update: Thanks for all your advice.
I checked connections and they all look clean and tight. I started the engine and it ran fine (16 degrees F outside). The interior volt meter read 11 volts again and the battery light was on. I then ran jumper cables to another car and the interior volt meter jumped to 12 or 13 V, but the battery light stayed on.
I took out the battery to have it tested. I'm not sure the age of the battery.
It sounds to me like the alternator. Doesnt the battery light come on when current is flowing out of the battery, meaning a lower voltage at the alternator? Putting a jump on the battery would simulate a good battery, if the light was still on, that would rule out your battery. Im curious to hear how it turns out.