In this contribution, we investigate the seasonal variation
of multi-muon events observed by the NO$\nu$A Near Detector (ND) at
Fermilab, using the general-purpose Monte Carlo code FLUKA-CERN to
simulate the transport and interaction of the air-shower particles
in the atmosphere and other media. Our atmospheric model uses air
densities for Winter and Summer averaged profiles calculated from
the temperature and geopotential information at 37 pressure levels
given by the European Center for Medium-Range Weather Forecasts
(ECMWF) datasets in situ. Our FLUKA geometry model also includes a
layered underground approximated to match the NO$\nu$A~ND and its
location. We compare our simulation results with the measured
seasonal flux modulation of multi-muon events by the
NO$\nu$A~ND. For the first time, we were able to describe the
multi-muon excess in Winter over Summer quantitatively and the
dependence on the multi-muon event multiplicity as observed by
NO$\nu$A. Finally, we compare our results for the muon flux at the
surface and detector level obtained from FLUKA simulations with the
previous work from other authors based on CORSIKA simulations. We
try to understand the reasons for the discrepancy by nearly a factor
of four between the results of two Monte Carlo codes.