  If a black hole has hair, how short can this hair be? A partial answer to
this intriguing question was recently provided by the 'no-short hair' theorem
which asserts that the external fields of a spherically-symmetric electrically
neutral hairy black-hole configuration must extend beyond the null circular
geodesic which characterizes the corresponding black-hole spacetime. One
naturally wonders whether the no-short hair inequality
$r_{\text{hair}}>r_{\text{null}}$ is a generic property of all electrically
neutral hairy black-hole spacetimes? In this paper we provide evidence that the
answer to this interesting question may be positive. In particular, we prove
that the recently discovered cloudy Kerr black-hole spacetimes --
non-spherically symmetric non-static black holes which support linearized
massive scalar fields in their exterior regions -- also respect this no-short
hair lower bound. Specifically, we analytically derive the lower bound
$r_{\text{field}}/r_+>r_+/r_-$ on the effective lengths of the external
bound-state massive scalar clouds (here $r_{\text{field}}$ is the peak location
of the stationary bound-state scalar fields and $r_{\pm}$ are the horizon radii
of the black hole). Remarkably, this lower bound is universal in the sense that
it is independent of the physical parameters (proper mass and angular harmonic
indices) of the exterior scalar fields. Our results suggest that the lower
bound $r_{\text{hair}}>r_{\text{null}}$ may be a general property of
asymptotically flat electrically neutral hairy black-hole configurations.
