  The accurate characterisation of the stellar magnetism of planetary host
stars has been gaining momentum, especially in the context of transmission
spectroscopy investigations of exoplanets. Indeed, the magnetic field regulates
the amount of energetic radiation and stellar wind impinging on planets, as
well as the presence of inhomogeneities on the stellar surface that hinder the
precise extraction of the planetary atmospheric absorption signal. We initiated
a spectropolarimetric campaign to unveil the magnetic field properties of known
exoplanet hosting stars included in the current list of potential Ariel
targets. In this work, we focus on HD 63433, a young solar-like star hosting
two sub-Neptunes and an Earth-sized planet. These exoplanets orbit within 0.15
au from the host star and have likely experienced different atmospheric
evolutionary paths. We analysed optical spectropolarimetric data collected with
ESPaDOnS, HARPSpol, and Neo-Narval to compute the magnetic activity indices
(log R'_HK , H$\alpha$, and Ca ii infrared triplet), measure the longitudinal
magnetic field, and reconstruct the large-scale magnetic topology via
Zeeman-Doppler imaging (ZDI). The magnetic field map was then employed to
simulate the space environment in which the exoplanets orbit. The reconstructed
stellar magnetic field has an average strength of 24 G and it features a
complex topology with a dominant toroidal component, in agreement with other
stars of a similar spectral type and age. Our simulations of the stellar
environment locate 10% of the innermost planetary orbit inside the Alfv\'en
surface and, thus, brief magnetic connections between the planet and the star
can occur. The outer planets are outside the Alfv\'en surface and a bow shock
between the stellar wind and the planetary magnetosphere could potentially
form.
