  The reactivity of interstellar carbon atoms (C) on the water-dominated ices
is one of the possible ways to form interstellar complex organic molecules
(iCOMs). In this work, we report a quantum chemical study of the coupling
reaction of C ($^3$P) with an icy water molecule, alongside possible subsequent
reactions with the most abundant closed shell frozen species (NH$_3$, CO,
CO$_2$ and H$_2$), atoms (H, N and O), and molecular radicals (OH, NH$_2$ and
CH$_3$). We found that C spontaneously reacts with the water molecule,
resulting in the formation of $^3$C-OH$_2$, a highly reactive species due to
its triplet electronic state. While reactions with the closed-shell species do
not show any reactivity, reactions with N and O form CN and CO, respectively,
the latter ending up into methanol upon subsequent hydrogenation. The reactions
with OH, CH$_3$ and NH$_2$ form methanediol, ethanol and methanimine,
respectively, upon subsequent hydrogenation. We also propose an explanation for
methane formation, observed in experiments through H additions to C in the
presence of ices. The astrochemical implications of this work are: i) atomic C
on water ice is locked into $^3$C-OH$_2$, making difficult the reactivity of
bare C atoms on the icy surfaces, contrary to what is assumed in astrochemical
current models; and ii) the extraordinary reactivity of $^3$C-OH$_2$ provides
new routes towards the formation of iCOMs in a non-energetic way, in particular
ethanol, mother of other iCOMs once in the gas-phase.
