The most likely cause of the problem you describe is sticking cables. Internal geared hubs also have cables. That may not make any difference at all.

A lot of people forget about condensation on metal parts when brining something cold into the house. This can get a little water into a cable housing, especially on ladies bikes due to the way the cables are run. Every time you bring a cold bike into the house you should clean the cables and let the bike dry overnight with the cables open or the housings moved to dry. Once you get water in a cable it can be very hard to get it out. And if you bring your bike in and out again, you start all over again. I have had derailleur bikes freeze the cables on a day when I went through a puddle and late in the day it was 29F. just cleaning out the cables fixed it.