  A frozen, solid helium core, dubbed snowball, is typically observed around
cations in liquid helium. Here we discover, using path integral simulations,
that around a cationic molecular impurity, protonated methane, the $^4$He atoms
are indeed strongly localized akin to snowballs but still participate in vivid
bosonic exchange induced by the ro-vibrational motion of the impurity. Such
combination of solid-like order with pronounced superfluid response in the
first helium shell indicates that manifestations of local supersolid behavior
of $^4$He can be induced -- and probed experimentally -- by charged molecules.
