  We give asymptotics for the number of Drinfeld $\mathbb{F}_q[T]$-modules over
$\mathbb{F}_q(T)$ of a given height, which satisfy prescribed sets of local
conditions. This is done by relating our problem to a problem about counting
points on weighted projective spaces. Our results for counting points of
bounded height on weighted projective spaces over global function fields may be
of independent interest.
