  We extend our previous work in which we derived the most general form of an
induced metric describing the geometry of an axially symmetric extremal
isolated horizon (EIH) in asymptotically flat spacetime. Here we generalize it
to EIHs in asymptotically (anti-)de Sitter spacetime. The resulting metric
conveniently forms a 6-parameter family which, in addition to a cosmological
constant $\Lambda$, depends on the area of the horizon, total electric and
magnetic charges, and two deficit angles representing conical singularities at
poles. Such a metric is consistent with results obtained in the context of
near-horizon geometries. Moreover, we study extremal horizons of all black
holes within the class of Plebanski-Demianski exact (electro)vacuum spacetimes
of the algebraic type D. In an important special case of non-accelerating black
holes, that is the famous Kerr-Newman-NUT-(A)dS metric, we were able to
identify the corresponding extremal horizons, including their position and
geometry, and find explicit relations between the physical parameters of the
metric and the geometrical parameters of the EIHs.
