  The local order around alkali (Li$^+$ and Na$^+$) and alkaline-eath (Be$^+$,
Mg$^+$ and Ca$^+$) ions in $^4$He clusters has been studied using ground-state
path integral Monte Carlo calculations. We apply a criterion based on multipole
dynamical correlations to discriminate between solid-like versus liquid-like
behavior of the $^4$He shells coating the ions. As it was earlier suggested by
experimental measurements in bulk $^4$He, our findings indicate that Be$^+$
produces a solid-like ("snowball") structure, similarly to alkali ions and in
contrast to the more liquid-like $^4$He structure embedding heavier
alkaline-earth ions.
