The Snare Dragon is mentioned only once, and, fortunately, has a cameo picture. When the reader is first introduced to Tantrum O'Ugerly, she sports a Snare Dragon nestled in her hair.

"UG's dear little daughter, Tantrum, was about six foot two with alot of flame-red hair and green eyes. A beautiful red Snare Dragon had made a nest on her head, and she was feeding it acorns."
How to Break a Dragon's Heart

The Snare Dragon is most likely a type of Hunting or Lap dragon, that evidently has an omnivorous diet.

Though not mentioned, the same Snare Dragon does appear again in the final book in the series, still on the same spot nestled in Tantrum's hair.