It's still not that cold unless they live outside. My little mixed hound is 14 and she only grows a few patches of winter fur on her flanks. I live in El Paso and we even had snow this year, but she lives inside.
All smooth dachshunds grow winter coats. However, when it reaches a certain period they shed a lot and at times it can be seen that the winter coats did not grow. Others shed moderately but others shed a lot. When you realize this, you only need to keep the coat neat and tidy.
Some species of dogs dont grow under coats. Some species are not originally from cold climates and do not have genes for undercoats. Chihuahuas dont either. My dog, who is a dachsund/chihuahua/papillion mix doesnt grow a winter coat either.