I've seen someone else posting about this "Pin the tail on the cow" thingy and mentioning the Christmas event, but personally I've done the entire Christmas event and gotten all the rewards and I never came across all this Cow business.
In a field just north of the farmer we gave pear tree to is a cowboy character. He askes for you to pin the tails on cows. You have to kill cows to get tails. The tailess cows just seem to be respawning.