Audi A6 '98 not cranking in cold weather
 

This winter I've had issues with my Audi not cranking when it gets cold out (it was around 0 F when I tried it recently and it wouldn't crank, then it started fine a day after that when it was around 25 F). All of the lights on the dash will turn on (including the battery symbol), but I get no noise at all.
I haven't had this problem before, but I did have an issue over a year ago where it would never crank, so I had to get the starter replaced. It worked fine after that. I didn't drive it almost at all during summer, but I got some good winter tires for it and was hoping to drive it now. The battery had gone completely dead twice over the summer, I think just from letting it sit. The battery is only around a year old, so I took it to the battery place and had them test it after it had gone dead a second time. They claimed it was just very low on charge but works fine when charged. It does seem to work fine now when it's warm.
I've also filled the oil up (it has a slow leak) with Mobil 1 0W40 and refilled the gas a few times since letting it sit.

I can't tell if this might be the starter, the battery (I know they lose capacity when it's cold) or something else. Does anyone know what it might be or have any advice for troubleshooting?

Thanks very much!