  We consider supersymmetric near-horizon geometries in heterotic supergravity
up to two loop order in sigma model perturbation theory. We identify the
conditions for the horizons to admit enhancement of supersymmetry. We show that
solutions which undergo supersymmetry enhancement exhibit an sl(2,R) symmetry,
and we describe the geometry of their horizon sections. We also prove a
modified Lichnerowicz type theorem, incorporating $\alpha'$ corrections, which
relates Killing spinors to zero modes of near-horizon Dirac operators.
Furthermore, we demonstrate that there are no AdS2 solutions in heterotic
supergravity up to second order in $\alpha'$ for which the fields are smooth
and the internal space is smooth and compact without boundary. We investigate a
class of nearly supersymmetric horizons, for which the gravitino Killing spinor
equation is satisfied on the spatial cross sections but not the dilatino one,
and present a description of their geometry.
