Although Shakespeare might be right in his statement about a certain amount of rottenness in Denmark, he certainly did not refer to the Danish cycle paths. The cycle path partly runs along the railway and through parks. Cycle signs are everywhere, and contrary to Norway the destination is clearly indicated on every signpost. The secret is raising your left arm before you stop, and keep well to the right if you go slowly. The Danes have a completely different attitude to cycling than Norwegians.
People go shopping, touring and commuting by bike all year round.
I once saw figures on daily commuting in Copenhagen - I don't remember any details but a substantial part of Danish economy is in fact based upon bicycling. This also means that the bicycle traffic regulations are expected not to be broken. In Norway the police will hardly ever give a fine to anyone riding without a light in the dark, while in Denmark you're likely to be stopped immediately. Personally I've been stopped by the police for pavement cycling - used as I am to Norway where there is often no other choice. Our tour ended with a couple of relaxing days visiting my brother and his family in Copenhagen, before returning to Oslo with the DFDS ferry.