  The LHC may produce light, weakly-interacting particles that decay to dark
matter, creating an intense and highly collimated beam of dark matter particles
in the far-forward direction. We investigate the prospects for detecting this
dark matter in two far-forward detectors proposed for a future Forward Physics
Facility: FASER$\nu$2, a 10-tonne emulsion detector, and FLArE, a 10- to
100-tonne LArTPC. We focus here on nuclear scattering, including elastic
scattering, resonant pion production, and deep inelastic scattering, and devise
cuts that efficiently remove the neutrino-induced background. In the
invisibly-decaying dark photon scenario, DM-nuclear scattering probes new
parameter space for dark matter masses 5 MeV $\lesssim m_{\chi} \lesssim$ 500
MeV. When combined with the DM-electron scattering studied previously,
FASER$\nu$2 and FLArE will be able to discover dark matter in a large swath of
the cosmologically-favored parameter space with MeV $\lesssim m_{\chi} \lesssim
$ GeV.
