  We characterize those mappings from a compact subset of $\mathbb{R}$ into the
Heisenberg group $\mathbb{H}^{n}$ which can be extended to a $C^{m}$ horizontal
curve in $\mathbb{H}^{n}$. The characterization combines the classical Whitney
conditions with an estimate comparing changes in the vertical coordinate with
those predicted by the Taylor series of the horizontal coordinates.
