  We study black hole solutions at first order in the Hartle-Thorne
slow-rotation approximation in Horndeski gravity theories. We derive the
equations of motion including also cases where the scalar depends linearly on
time. In the Hartle-Thorne formalism, all first-order rotational corrections
are described by a single frame-dragging function. We show that the
frame-dragging function is exactly the same as in general relativity for all
known black hole solutions in shift symmetric Horndeski theories, with the
exception of theories with a linear coupling to the Gauss-Bonnet invariant. Our
results extend previous no-hair theorems for a broad class of Horndeski gravity
theories.
