Dragon rider dystopia

I had found a book with an interesting setting. It took place in world ravaged by dragons. The remaining humans holed themselves up in scattered settlements called "cities", though on the surface they looked more like small towns and villages. It seemed many lived underground. Individuals known as "surgeons" (for whatever reason) had the job of ferrying supplies between cities using transport planes and flying fortresses. It was dangerous work.

The biggest danger was how the dragons could project a hypnotic power of suggestion to bend humans to their will. They could also take human forms and infiltrate population centres. However, defeating a dragon in battle would cause it to become subservient to the victor.

The protagonist was passing over City One (it was winter and blanketed with snow) which appeared abandoned from above. It may have been recently attacked. They were flying on the back of a dragon they had defeated the previous year and were on their way to an old church to take out, and perhaps even attempt to reason with, one lurking inside.

I don't remember much more about it, but the book seemed to play with the idea that the whole subservience thing could just be the dragon playing along and that they're not to be trusted, though it never answered that question explicitly.