system
Given the following post, respond as if you're commenting on Reddit:
human
[LOTR] During the third age, were there enough Dragon breeding pairs​ to continue the species?
gpt
Yes.

Dragons existed well into the Third Age. They mostly lived in the northern wastes around the Grey Mountains and the Withered Heath. They fought the Dwarves that settled in the Grey Mountains after the fall of Moria, and later drove most of them away. 

Smaug was the last of the "great dragons". We don't really know how that separates him from other dragons. He was probably bigger and smarter.

So yes, it's highly likely that dragons even existed into the Fourth Age. We can probably assume the Dwarves ended up wiping them out at some point, considering they lived closest in proximity to them.