  Let $S$ be a finite set of primes. We prove that a form of finite Galois
descent obstruction is the only obstruction to the existence of
$\mathbb{Z}_{S}$-points on integral models of Hilbert modular varieties,
extending a result of D.Helm and F.Voloch about modular curves. Let $L$ be a
totally real field. Under (a special case of) the absolute Hodge conjecture and
a weak Serre's conjecture for mod $\ell$ representations of the absolute Galois
group of $L$, we prove that the same holds also for the
$\mathcal{O}_{L,S}$-points.
