Mixtures of water and poly(vinyl alcohol) (0-96%) have been investigated using molecular dynamics simulations with an atomistically detailed force held. The concentration and temperature (300 and 375 K) dependence of a number of dynamical processes has been studied : Water diffusion including its mechanism, water reorientation and its anisotropy, formation and destruction of hydrogen bonds, water clustering, dielectric properties, local mobility of the polymer. The time scales of these processes extend over several orders of magnitude. Their concentration dependence ranges from no dependence at all to higher than exponential dependence. The quantitative and qualitative results show good agreement with experimental values where available. Comparisons are made with previous simulations of an apolar polymer-solvent mixture (benzene-polystyrene). They indicate, that in spite of the substantial difference in interactions there are qualitative features common to both systems and probably generic to swollen polymers.