Variational Monte Carlo and diffusion Monte Carlo calculations have been carried out for cations such as Li(+), Na(+), and K(+) as dopants of small helium clusters over a range of cluster sizes up to about 12 solvent atoms. The interaction has been modeled through a sum-of-potential picture that disregards higher order effects beyond atom-atom and atom-ion contributions. The latter were obtained from highly correlated ab initio calculations over a broad range of interatomic distances. This study focuses on two of the most striking features of the microsolvation in a quantum solvent of a cationic dopant: electrostriction and snowball effects. They are discussed here in detail and in relation with the nanoscopic properties of the interaction forces at play within a fully quantum picture of the cluster features.