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.