  Lipschitz light maps, defined by Cheeger and Kleiner, are a class of
non-injective "foldings" between metric spaces that preserve some geometric
information. We prove that if a metric space $(X,d)$ has Nagata dimension $n$,
then its "snowflakes" $(X,d^\epsilon)$ admit Lipschitz light maps to
$\mathbb{R}^n$ for all $0<\epsilon<1$. This can be seen as an analog of a
well-known theorem of Assouad. We also provide an application to a new variant
of conformal dimension.
