I have no idea what that reindeer is? Kicchou?

Yes I think so too. The horns match and that thing on her head matches the shell that Kicchou Yachie has on her back.

To dispel any doubt, the mysterious yukkuri in panel 2 says:
Mogooooo!!! (Yachie is not mister reindeer!!!)

I can't add notes myself right now, so feel free to make it yourself if you want.