  Deviations from Gaussianity in the distribution of the fields probed by
large-scale structure surveys generate additional terms in the data covariance
matrix, increasing the uncertainties in the measurement of the cosmological
parameters. Super-sample covariance (SSC) is among the largest of these
non-Gaussian contributions, with the potential to significantly degrade
constraints on some of the parameters of the cosmological model under study --
especially for weak lensing cosmic shear. We compute and validate the impact of
SSC on the forecast uncertainties on the cosmological parameters for the Euclid
photometric survey, obtained with a Fisher matrix analysis, both considering
the Gaussian covariance alone and adding the SSC term -- computed through the
public code PySSC. The photometric probes are considered in isolation and
combined in the `3$\times$2pt' analysis. We find the SSC impact to be
non-negligible -- halving the Figure of Merit of the dark energy parameters
($w_0$, $w_a$) in the 3$\times$2pt case and substantially increasing the
uncertainties on $\Omega_{{\rm m},0}, w_0$, and $\sigma_8$ for cosmic shear;
photometric galaxy clustering, on the other hand, is less affected due to the
lower probe response. The relative impact of SSC does not show significant
changes under variations of the redshift binning scheme, while it is smaller
for weak lensing when marginalising over the multiplicative shear bias nuisance
parameters, which also leads to poorer constraints on the cosmological
parameters. Finally, we explore how the use of prior information on the shear
and galaxy bias changes the SSC impact. Improving shear bias priors does not
have a significant impact, while galaxy bias must be calibrated to sub-percent
level to increase the Figure of Merit by the large amount needed to achieve the
value when SSC is not included.
