  We determine the asymptotic symmetry group of Killing horizons by choosing
Gaussian null coordinates in the neighbourhood of the horizon and boundary
conditions that respect the leading order terms in the metric. The analysis
divides naturally into the two cases of subextremal and extremal horizons. In
general, we find rather involved asymptotic symmetry generators that
nevertheless involve supertranslations and Killing vectors on the compact
horizon. The most striking observation is the difference in the dependence on
the coordinate along the horizon; we relate this to the redshift effect for
subextremal horizons. We consider the spherically symmetric case as a special
and illuminating example.
