Definitely worth getting the battery checked. It can be done for free at Halfords or similar. If it's not the battery then a diagnostic check is recommended.
I'd definitely put it down to outside temperature. I know my older A6 takes longer to start in cold mornings. You could always get a diagnostic check to see if everything is working as it should.
Welcome to the forum you'll find the members on here are a friendly and helpful bunch 🙂
The V6 diesel A4 would have had the same engine as my A6.
Nice to see youve had a few different Audi's 🙂
This link might help:
https://www.audi-sport.net/xf/threads/dab-radio-signal-suddenly-very-poor.349691/
It could be the amplifier. Or have you fitted a dash cam lately?
Honestly I'm not sure, but I imagine both should work if you've got 2 fitted. If it's not working it could be down to a failed sensor or broken wire maybe?