Yes, it's cold. This is Scandinavia, and it's winter.
"There is no such thing as bad weather, only inappropriate clothing." This saying has always annoyed me - I disagree. 'Too wet' and 'too cold' (even 'too hot') are definitely factors that will have me spending the majority of my time indoors.
But only the majority of my time, not all of it. I jump at the chance for a walk, especially if the sun is out. The fresh air clears the cobwebs from my mind. My ears may be numb afterwards, but that just makes curling up in a sofa with a hot cup of [insert favourite beverage] that much more enjoyable.
There is no such thing as a bad time of year to be in Copenhagen.
Photos are from the park 'Frederiksberg Have', in the background Frederiksberg Slot and the Zoo. They were taken a late afternoon in January, there were plenty of people around - especially children with sledges.