  It has long been known that strings wound around incontractible cycles can
play a vital role in cosmology. In particular, in a spacetime with toroidal
spatial hypersurfaces, the dynamics of the winding modes may help yield three
large spatial dimensions. However, toroidal compactifications are
phenomenologically unrealistic. In this paper we therefore take a first step
toward extending these cosmological considerations to $D$-dimensional toroidal
orbifolds. We use numerical simulation to study the timescales over which
"pseudo-wound" strings unwind on these orbifolds with trivial fundamental
group. We show that pseudo-wound strings can persist for many ``Hubble times''
in some of these spaces, suggesting that they may affect the dynamics in the
same way as genuinely wound strings. We also outline some possible extensions
that include higher-dimensional wrapped branes.
