If you live in an area where your pet is exposed to long cold winters it is best to be prepared for the season.  Many smaller dogs can have trouble adjusting to the normal duties of going outside for potty time due to the cold.  Many do not like the cold and this can make it difficult on you the owner when you are attempting to deal with taking them out during this time.  Be understanding of the situation, if you have to image what it is like for you to go outside with no socks and shoes on during the cold snowy days.  This can be difficult for you to accomplish so understand that it is not them being difficult rather it is them having a hard time dealing with the climate change.
It may be something for you as the owner to make note of that this is a time that should be addressed with possibly training your pet to go on alternate means.  For example putting hay in a garage on top of some plastic wrap may be a good place for them to go.  Or getting any one of the many products online available for indoor use such as the indoor potty places.