Combinatorial Hopf algebra of superclass functions of type $D$

We provide a Hopf algebra structure on the space of superclass functions on the unipotent upper triangular group of type D over a finite field based on a supercharacter theory constructed by Andr'e and Neto. Also, we make further comments with respect to types B and C. Type A was explores by M. Aguiar et. al (2010), thus this paper is a contribution to understand combinatorially the supercharacter theory of the other classical Lie types.