  In full Horndeski theories, we show that the static and spherically symmetric
black hole (BH) solutions with a static scalar field~$\phi$ whose kinetic
term~$X$ is nonvanishing on the BH horizon are generically prone to
ghost/Laplacian instabilities. We then search for asymptotically Minkowski
hairy BH solutions with a vanishing $X$ on the horizon free from
ghost/Laplacian instabilities. We show that models with regular coupling
functions of $\phi$ and $X$ result in no-hair Schwarzschild BHs in general. On
the other hand, the presence of a coupling between the scalar field and the
Gauss-Bonnet (GB) term $R_{\rm GB}^2$, even with the coexistence of other
regular coupling functions, leads to the realization of asymptotically
Minkowski hairy BH solutions without ghost/Laplacian instabilities. Finally, we
find that hairy BH solutions in power-law $F(R_{\rm GB}^2)$ gravity are plagued
by ghost instabilities. These results imply that the GB coupling of the form
$\xi(\phi)R_{\rm GB}^2$ plays a prominent role for the existence of
asymptotically Minkowski hairy BH solutions free from ghost/Laplacian
instabilities.
