There's a number of pets you'll just find in the world, but some will only spawn when it's raining, or the winter time, for example. I just put one in the other day that only spawns between 9 pm and midnight--during that time he pops every 15 min. It's a really limited period, and you can imagine people in town talking about it when it spawns.
Has anyone found it yet? I have a feeling it might be the Gurkster. Or is it the Restless Shadeling?