Jerry Springer's Paternity Tests of Heat Miser and Snow Miser

In Rankin and Bass's The Year Without a Santa Claus, Snow Miser refers to Heat Miser as his step brother, but they both fawn over Mother Nature. Logically, if they are step-brothers they are unrelated and can't both be Mother Nature's children. I can see them being half-brothers (both Mrs. N's kids, but with clearly different fathers.) Even so, I am starting to suspect the whole story was just made up.