We study the supersymmetric solutions of the simplest $N=2$ supersymmetrization of the Einstein-Yang-Mills theory in $d=4$: $N=2,d=4$ Super-Einstein-Yang-Mills theories. Given a solution of the standard Bogomol'nyi equations in $mathbf{R}^3$ (such as the well known 't Hooft-Polyakov $SU(2)$ monopole in the BPS limit) it is always possible to construct a supersymmetric solutions of the $N=2,d=4$ Super-Einstein-Yang-Mills theory. We study which gravitating solutions can be constructed using 't Hooft-Polyakov $SU(2)$ monopole in the BPS limit and other solutions of the Bogomol'nyi equations. From the 't Hooft-Polyakov $SU(2)$ monopole one gets a globally regular solution (a ``global monopole''). From the other solutions, which are usually disregarded because they are singular in $mathbf{R}^3$, one gets regular black holes with non-Abelian hair whose event horizons hide the singularities. All the solutions are given in a purely analytical form.