Does the sky get darker faster during the winter?
The further north you go, the time between sunset and darkness becomes longer, no matter the season. The reason is due to the velocity at that latitude. If there is 10 min of twilight on the equator, then there is $10\sqrt{2}$ min at 45° latitude, 20 min at 60° latitude, ...

Added:
I used the website that @barrycarter listed above and discovered that there are 2 maxima and minima during the year. The solstices have the longest twilight times and the equinoxes have the shortest twilight times.