We show that constant mean curvature hypersurfaces in $\mathbb{H}^n\times\mathbb{R}$, with small and pinched boundary contained in a horizontal slice $P$ are topological disks, provided they are contained in one of the two halfspaces determined by $P$. This is a joint work with B. Nelli and it is the analogous in $\mathbb{H}^n\times\mathbb{R}$ of a result in $\mathbb{R}^3$ by A. Ros and H. Rosenberg.