Horsefeathers

The "nonsense" sense is horse + feathers, a nonexistent item, as only birds have feathers. Compare henâ€™s teeth.

The "horse hair" sense notes the similarly of that hair to bird feathers.

Regarding the roofing sense, compare feathering strip and horsefeathers.

Full definition of horsefeathers

(euphemistic) Indicates disbelief.Horsefeathers! You knew it was a bad idea and now you're just making excuses about it.

(plural only)

(euphemistic) Nonsense; indicates disbelief.Dismissing the rumors as "horsefeathers", he advised everybody to disregard them.
Long hair on lower legs of a draft horse (e.g., Clydesdale), especially the rear legs.
Feathering strips.

1940 New York lumber trade journal - Vol.108-9, p.26:The exterior of the court is entirely of sheathing and wood shingles applied over "horsefeathers."
1968 United States Customs Court, First Division, A. N. DERINGER, INC. v. UNITED STATES 287 F.Supp. 1016 (1968) August 8, 1968:In summary, the record establishes that to produce horsefeathers one starts by sawing a log (longitudinally) into boards or planks, which are then likewise center resawn (longitudinally); that the original boards, as well as the center resawn boards, have at least two approximately parallel longitudinal sawed surfaces; that the resawn boards are simply resawn again longitudinally at an angle or bevel to produce horsefeathers; and that the only other sawing required is the crosscutting of the boards to length.
1978 Joseph R. Provey "How to reroof your house like a pro" Popular Mechanics, April 1978, p.160:Feathering strips, called horsefeathers, can be used to level cedar-shingle roof before reroofing with asphalt shingles
2005 Daniel Benn Atcheson, Roofing Construction and Estimating Craftsman Book Company, p.192:To install shakes or shingles over beveled siding, fill in the low points of the existing wall with lumber or plywood strips (called horse feathers).

In â€œhorse hairâ€ sense, often referred to instead as feather, feathers or feathering, with hair on the front part narrowly referred to as spats.