  We study regular and black hole solutions to the coupled classical
Einstein--Yang-Mills--Higgs system. It has long been thought that black hole
solutions in the spontaneously broken phase of such a theory could have no
nontrivial field structure outside of the horizon. We first show that the
standard black hole no-hair theorem underlying this belief, although true in
the abelian setting, does not necessarily extend to the non-abelian case. This
indicates the possibility of solutions with non-trivial gauge and Higgs
configurations decaying exponentially {\it outside} the horizon. We then find
such solutions by numerical integration of the classical equations for the case
of $SU(2)$ coupled to a Higgs doublet (the standard model less hypercharge).
  As a prelude to this work we also study regular and black hole solutions to
Einstein--Non-Abelian--Proca theory and as a postscript we briefly discuss the
important issue of stability.
