  Whereas subriemannian geometry usually deals with smooth horizontal
distributions, partially hyperbolic dynamical systems provide many examples of
subriemannian geometries defined by non-smooth (namely, H\"older continuous)
distributions. These distributions are of great significance for the behavior
of the parent dynamical system. The study of H\"older subriemannian geometries
could therefore offer new insights into both dynamics and subriemannian
geometry. In this paper we make a small step in that direction: we prove a
H\"older-type lower bound on the subriemannian distance for H\"older continuous
nowhere integrable codimension one distributions. This bound generalizes the
well-known square root bound valid in the smooth case.
