I'm not sure if anyone has noticed already, but the Horse King has a weird bug on Carrots.
I'm pretty sure before it added 1000% healing effectiveness to Carrots, and then it was removed eventually. However, when you wear a Horse King together with the Rudolph Hairband, the Horse King's nullification to the Carrot healing effectiveness increase completely ignores Rudolph Hairband's Carrot buff. Therefore, a Carrot's healing effectiveness when wearing both headgears isn't increased whatsoever.