What gives mass to black hole? I like to know when a dying star collapsed into a black hole, is there anything inside or on the event horizon that is interacting with higgs field? 
 A: It is important to understand that energy can have mass as well. For example 99% of the mass of the proton is due to the binding energy of the quarks inside it. Only about 1% comes from the interaction of the quarks with the Higgs field. So only the masses of the elementary particles are due entirely to the Higgs field. Since a black hole is a bound state not an elementary particle we don't need to invoke the Higgs field to explain all its mass.
General Relativity treats mass and energy as equivalent and related by Einstein's famous equation $E=mc^2$. Both mass and energy contribute to the curvature of spacetime. So while we talk about a black hole having a mass of $M$, we could equally well talk about it having an energy of $Mc^2$. Both are the same in GR. This means we do not need to invoke the Higgs field to explain the gravitational field of a black hole, or indeed any massive object. We could have constructed our black hole from massless photons and it would still have a mass $M$ related to the energy $E$ we put into it by $E=Mc^2$.
So the bottom line is that we don't need to worry about the Higgs field when working with calculations in GR. This is just as well since we do not have a theory of quantum gravity, so the problem of reconciling gravity with quantum field theory is currently unsolved. We live in hope that as and when we do understand quantum gravity it will become clear how the Higgs field is involved.
A: To answer the question in the title of this post: the mass of a black hole, and the gravitational field propagated by that mass, come from the mass of the object which originally collapsed and formed the black hole, plus any mass which fell into it after that. 
Since the gravitational field of a black hole was in existence before the hole itself was formed, then there seems to be no need to invoke the specific dynamics of the higgs mechanism at the event horizon to account in some way for the mass of the black hole. 
