  The concept of "Isolated Horizon" has been recently used to provide a full
Hamiltonian treatment of black holes. It has been applied successfully to the
cases of {\it non-rotating}, {\it non-distorted} black holes in Einstein
Vacuum, Einstein-Maxwell and Einstein-Maxwell-Dilaton Theories. In this note,
it is investigated the extent to which the framework can be generalized to the
case of non-Abelian gauge theories where `hairy black holes' are known to
exist. It is found that this extension is indeed possible, despite the fact
that in general, there is no `canonical normalization' yielding a preferred
Horizon Mass. In particular the zeroth and first laws are established for all
normalizations. Colored static spherically symmetric black hole solutions to
the Einstein-Yang-Mills equations are considered from this perspective. A
canonical formula for the Horizon Mass of such black holes is found. This
analysis is used to obtain nontrivial relations between the masses of the
colored black holes and the regular solitonic solutions in Einstein-Yang-Mills
theory. A general testing bed for the instability of hairy black holes in
general non-linear theories is suggested. As an example, the embedded Abelian
magnetic solutions are considered. It is shown that, within this framework, the
total energy is also positive and thus, the solutions are potentially unstable.
Finally, it is discussed which elements would be needed to place the Isolated
Horizons framework for Einstein-Yang-Mills theory in the same footing as the
previously analyzed cases. Motivated by these considerations and using the fact
that the Isolated Horizons framework seems to be the appropriate language to
state uniqueness and completeness conjectures for the EYM equations --in terms
of the horizon charges--, two such conjectures are put forward.
