Last winter, Mr Plow was added to the game (for 90 donuts) so it was only a matter of time before a Plow King costume for Barney was created. You can’t buy this costume though, you have to earn it as one of the prizes on the Holiday Wheel. Though it does seem to make it appear you will have to win the Mr. Plow costume first.
So what happens if you don’t have Barney and you win the costume? It may just stay in your inventory, should you ever decide to purchase the Bowlarama. There is a possibility of that you can acquire him after unlocking the Plow King’s Plow, but that is only speculation.
Unlocking the Plow King costume sets off a five-part quest line, which you can follow along with in both abridged and unabridged form. It’s a bit odd how he only monologues to himself in this quest line. Perhaps the whole experience are just the inner-thoughts of a man who has been drinking too much alcohol.