Laptop battery charge level suddenly dropped from over 50% to 1% at approx. 4 ° C - is that normal (battery 7 years old, permanently installed)?

So normally my battery would last about 30 minutes after 7 years if I work normally with my laptop (before it was 5 hours).

Today I packed the laptop at about half charge and then turned it on after lying around at 3-4 ° C for a few hours - it went out almost immediately, I could only see that the charge indicator even ZERO (0 )% displayed.

Is something "normal" with a battery of this age?

Yes, this is normal with the temperatures and the age of the battery.