[Hookbill the Goomba]

I think we have to assume that some Dragons survived after Smoug was defeated. As Thorin says;

There were many Dragons in the North.
Thorin: The Hobbit, An unexpected party

We aren’t told what happened to these dragons though. If the dragons were around in the north which we can guess to ether be the northern waste, blue mountains, or Helcar. These wide lands may be suited to Dragons.
The reasons behind Sauron not using the dragons is perhaps because he did not think that they would be useful in a battle situation, After Smoug was defeated, perhaps the other dragons weren’t considered as much as a threat. Dragons were not very trust worthy, Glourong often desolated even the orcs that were supposed to be helping him, and Perhaps Sauron did not want to risk the same.