Their generators are almost certainly tested frequently. But there could be any number of causes underlying the failure, and unfortunately sometimes failure does happen.
The problem is usually not "not reliable in cold" but rather, the generators are X years old and the temperature is now changing in Europe from "mostly warm" to "warm over the day and icecold in the night" and finally aiming for "icecold all day", which means any equipment exposed will go through rather severe temperature changes.
While generators are usually able to handle this with sufficiently low failure risk, the risk is increase due to the changing temperature
It wasn't even freezing overnight at Strasbourg [1], I doubt that the cold could cause any effects at 5C. Maybe they were run once a month but never tested under load? 2x20kv lines failing will have put them at near maximum load immediately, perhaps they weren't designed for that.
Improbable. Even in a mostly-normal office building, the monthly generator test consisted essentially of "cut the mains power and see that no impact is perceived as UPS, batteries, and autostarted generators bear the load, in their turn for ~2 hrs total."