  Minimal algebraic surfaces of general type $X$ such that
$K^2_X=2\chi(\mathcal{O}_X)-6$ or $K^2_X=2\chi(\mathcal{O}_X)-5$ are called
Horikawa surfaces. In this note we study $\mathbb{Z}^2_2$-actions on Horikawa
surfaces. The main result is that all the connected components of Gieseker's
moduli space of canonical models of surfaces of general type with invariants
satisfying these relations contain surfaces with $\mathbb{Z}^2_2$-actions.
