  We apply a population-orbit superposition method to 16 galaxies in the Fornax
cluster observed with MUSE/VLT in the context of the Fornax3D project. By
fitting the luminosity distribution, stellar kinematics, and age and
metallicity maps simultaneously, we obtained the internal stellar orbit
distribution, as well as the age and metallicity distribution of stars on
different orbits for each galaxy. Based on the model, we decompose each galaxy
into a dynamically cold disk (orbital circularity $\lambda_z\ge0.8$) and a
dynamically hot non-disk component (orbital circularity $\lambda_z<0.8$), and
obtain the surface-brightness, age, and metallicity radial profiles of each
component. The galaxy infall time into the cluster is strongly correlated with
galaxy cold-disk age with older cold disks in ancient infallers. We quantify
the infall time $t_{\rm infall}$ of each galaxy with its cold-disk age using a
correlation calibrated with TNG50 cosmological simulations. For galaxies in the
Fornax cluster, we found that the luminosity fraction of cold disk in galaxies
with $t_{\rm infall}>8$ Gyr are a factor of $\sim 4$ lower than in more recent
infallers while controlling for total stellar mass. Nine of the 16 galaxies
have spatially extended cold disks, and most of them show positive or zero age
gradients; stars in the inner disk are $\sim 2-5$ Gyr younger than that in the
outer disk, in contrast to the expectation of inside-out growth. Our results
indicate that the assembly of cold disks in galaxies is strongly affected by
their infall into clusters, by either removal of gas in outer regions or even
tidally stripping or heating part of the pre-existing disks. Star formation in
outer disks can stop quickly after the galaxy falls into the cluster, while
star formation in the inner disks can last for a few Gyrs more, building the
positive age gradient measured in cold disks.
