Thanks for the prompt responses folks.
I thought it was just a breather, because it has no clamp or barb marking / stretching on it, but I obviously wanted to make sure, as it is clearly related to the coolant. I couldn't find a barb, but could find a place where it tucked in behind the oil filter.
However, I also found a chunk of broken metal that had been the round bottom of a mount at the bottom of the bike and was like, "whoa now, what is this all." and ran right along to ask the grownups what was happening. =)
The broken mount arc was determined to be from a footpeg (NEXT TIME DON'T RIDE DIRT LIKE A WILD MONKEY) and I wanted new footpegs anyway.