This happens at the 1st start of the day. All the warning lights flash at start up like normal,but after the engine runs for a couple seconds,the battery light comes back on for a few seconds then goes back off and stays off. It only does this on a cold start,not after the engine is warmed up. Is my alternator failing?

Its a definite possibility. another possibility is that you simply have a loose connection somewhere. what I would do: pull the insulator on the positive stud of the alternator back just a little and probe with a voltmeter. the voltage directly on the stud should be around 14 volts. If it is, you should be ok, then its time to start checking wires. the first and most important being that very same alternator stud itself, battery terminals, and starter terminals, make sure they are all tight.