I am new to this site and honestly, I really have no idea if I'm posting this in the right area.
I have a 2004 Yukon Denali with 145k miles and have never had any issues with it. It'* been a great vehicle for the family. However, recently, it'* had some battery related issues. If I let it sit in the garage for a day or two, the battery is always dead. I charge it or give it a jump and it starts right up. Today I took it out and when I went to stop for a train, it started to shake a bit, the lights dimmed and it shut off. So I put it in park and started it up again. I took it straight to o'reilly auto parts where they tested both the battery and the alternator. Both tested out to be good. The employee told me that the fuel filter probably needs to be changed and reccomended that I put some Seafoam in the gas tank. On the way home, everything was working fine (Note that I hadn't put the Seafoam in yet, I was going to do it once I got home). Even when I stopped, everything seemed normal. So now I'm stuck here wondering if it'* a fuel issue or a battery issue. I do know that the battery is fairly old and probably needs to be changed anyway. Also, it has been extremely cold here.. ranging from -2 to 12 F and my battery seems to have more issues the colder it is. Could the vehicle have just died because of the cold weather and then worked fine after the engine had warmed up? Could the fuel pump be going out?
TIA everyone. Sorry if this post sounds like an obvious fix. I'm not exactly car savvy and am a complete worry-wart.

the lesson here is dont listen to counter parts people. the batteries test good sometimes when they are bad. also sometimes just the wires need to be cleaned. also many times the alt goes the same time the battery because the bad battery puts alot of stress on it. but i would save that for last because its not every time. with new battery and clean cables the battery should read 13-14.5(just after starting) at the battery. im not sure when they started using the pcm controlled alt but yours probably has it, so after the battery charges for a while it may come back down to 12-13.

If it'* the original battery it probably needs to be replaced. If a battery goes completely dead and freezes it'll never come back to life. I just had to replace the battery in my truck due to that. Left my GPS plugged in and we had -20F temps for about 3 days, truck sat for nearly a week and the battery was stone dead. Charged it up and drove it, turned it off and the next morning it'd only click. Another thing to check if you change the battery is the positive post, Have seen them rot right out of the battery. As soon as you put a wrench on the post and go to loosen it sometimes they pull right out. Also make sure the connections are clean like stated above.

If the weather has been that cold and you don't drive it that often there is a good possibility you could have some moisture that is freezing in your fuel lines. I had this happen to my 2000 Z71 and it would stall at stop lights. I know this doesn't fix your battery issue, but it would be worth putting a can of heat in your tank. Also make sure you never let your tank go below a 1/4 when it is wicked cold.