  We study 4-dimensional charged and static black holes in a generalized
scalar-tensor gravity model, in which a shift symmetry for the scalar field
exists. For vanishing scalar field the solution corresponds to the
Reissner-Nordstr\"om (RN) solution, while solutions of the full scalar-gravity
model have to be constructed numerically. We demonstrate that these black holes
support galilean scalar hair up to a maximal value of the scalar-tensor
coupling that depends on the value of the charge and can be up to roughly twice
as large as that for uncharged solutions. The Hawking temperature $T_{\rm H}$
of the hairy black holes at maximal scalar-tensor coupling decreases
continuously with the increase of the charge and reaches $T_{\rm H}=0$ for the
highest possible charge that these solutions can carry. However, in this limit,
the scalar-tensor coupling needs to vanish. The limiting solution hence
corresponds to the extremal RN solution, which does not support regular
galilaen scalar hair due to its AdS$_2\times S^2$ near-horizon geometry.
