Depends on the quality of the fossil deposits, foremost. Thin sediments with fast aggregation and bad living conditions for decomposer bacterias, such as volcanic ashes from an eruption, allow many details to be preserved, including hair and feather barbs. However, those fossils are a super tiny minority of what already is a super tiny minority of every living creature ever. Therefore, it is possible that a dinosaur with wig-like downs has existed, but every trace of these downs have disappeared.

then the mom dino got a karen haircut and said she isn't gonna vaccinate her children
that's how the dinos got wiped out