  Consider a stationary Poisson process of horospheres in a $d$-dimensional
hyperbolic space. In the focus of this note is the total surface area these
random horospheres induce in a sequence of balls of growing radius $R$. The
main result is a quantitative, non-standard central limit theorem for these
random variables as the radius $R$ of the balls and the space dimension $d$
tend to infinity simultaneously.
