  We consider a class of possibly degenerate second order elliptic operators
$\cal
  A$ on $\R^n$. This class includes hypoelliptic
  Ornstein-Uhlenbeck type operators having an additional first order term with
unbounded coefficients. We establish global Schauder estimates in H\"older
spaces both for elliptic equations and for parabolic Cauchy problems involving
${\cal A}$. The H\"older function spaces are defined with respect to a
non-euclidean metric related to the operator $\cal A$.
