Manuel asked: "Is there any other metric which contains a repulsive event horizon with negative mass?"
There is the Reissner Nordström repulsion where the charge has a repulsive gravitational effect, but the mass is positive and the sign of the charge doesn't matter. You still can't leave the black hole though after you fell in, but you also can't reach the singularity, unless you are a photon. It has the same effect as negative mass though inside of the critical radius, here we're talking about the effective mass:
Andrew Hamilton (GR, Black Holes & Cosmology 2017, p. 188) wrote: "Inside this radius the interior mass is negative, and the velocity is imaginary. The singularity is timelike, and infinitely gravitationally repulsive, unlike the central singularity of the Schwarzschild geometry."
The cosmic event horizon is also repulsive, but not due to negative mass, although dark energy has negative pressure, but positive density. Since pressure $\rm p$ acts $3\times$ stronger than density $\rho$ and for dark energy $\rm p=-\rho$ its net effect is $2\times$ as repulsive as the attraction you'd expect from its density alone. Therefore the expansion of the universe became accelerated roughly $6$ billion years ago when the dark energy density was half the matter density, but both positive.
Manuel wrote: "Intuitively, a big negative point mass should also create a repulsive event horizon, i.e., a region of spacetime that cannot be traversed from outside, due to respulsive gravity."
The Schwarzschild horizon with positive mass is due to $g_{\rm tt}=g^{\rm rr}=0$. With negative mass this terms can get large, but never zero. So the kinetic energy required to get farther in gets higher, but you still can reach the center with the speed of light, or come arbitrary close to it if your kinetic energy is arbitrary high. That is the case for negative mass singularities as well as for the Reissner Nordström repulsion.
