I think he does and he doesn't. Horn practically worshipped Silk as a boy, wrote a book about him, has invested much of his life in perpetuating his myth and doesn't feel up to "walking in his shoes." He knows that it is his--Horn's--personality in this body, however much Oreb may squawk. Nevertheless, parts of Silk are left, just as you can never erase a program completely from your computer.
When the "astral projection" trips are taken, the people at the other end appear as filtered through the mind not only of Silk/Horn, but that of the inhuma who he is partnered with (this is not something he can do alone). That is why he looks more like the old Horn, whose face he saw in the mirror when he shaved for decades, why the vampires are "real girls," why Oreb is so large and so human looking.
But something else is going on too. Horn is the first of Wolfe's characters ever to grow. The two-dimensional "plain man" of the first book, whose weaknesses were evident enough--just think Sinew, Krait, Seawrack--is slowly becoming more extraordinary than any other Wolfe character (not surprising, as we realize that he incorporates Silk and is an aspect of the Conciliator--you realize that his astral trip to Urth will be remembered as a visit from the Conciliator). This is the first Wolfe book that has ever made me cry, and I can cry all over again thinking of his silent and near-deadly heroism in cradling the dying Fava in his arms while they embark on one last adventure together. Or the last paragraph of the book, which is extraordinary. Horn is the best of Wofe's heroes, the deepest, the most human, the most adult.
-alga
*This is WHORL, for discussion of Gene Wolfe's Book of the Long Sun.