I have a 2009 Murano, and something similar happened to me....after having the battery replaced and the alternator evaluated, 3 times.
The problem was finally found to be the ground from the battery to the chassis was weak/rusty, I cleaned up all the ground wires that I could find.... battery, relays, etc...and then noticed that the transmission housing had a vacuum leak, and I replaced all vacuum hoses and my Murano runs like new. 133,000 miles and 31.0mpg at 40 and mph with 1100rpms smooth shifting
Your symptoms are that of a bad battery or alternator...
Have both checked to be sure they are performing correctly.
Most likely the brand new alternator you referred to was really a remanufactured alternator. It's not uncommon for them to fail shortly after installation... Have it checked, and have a warranty replacement installed if it's found to be faulty.
It was at auto zoneYour symptoms indicate you most likely have an alternator or battery issue... My guess is your alternator based on what you have posted.
Make sure the battery terminal are totally free of corrosion and snug.
Have both you battery and alternator checked at another place. It sounds like the place you went to got the battery diagnose wrong at first, I wouldn't trust their alternator diagnose... What place was it?
Cold weather shouldn't matter if both your battery and alternator are performing optimally. It will, however, further exasperate an existing issue...
Ok I'll take back to auto zone for another test it on came back as my ... Cadillac converter ... The last time I went but that can't be the problem right ???When the dash show the baterry and brake light you have not to change the battery, first. Please readout the codes in you car using scanner. You and other need to know first the code you car repot. Also. with the scanner Erase the codes. Drive about 15 minuts and check if any code continue. If so we'll make the next step. Good luck