The present invention provides golf balls having a rubber core, and a cover layer made from a thermoset polyurethane of polyurethane-urea that is the reaction product of a polyisocyanate with moisture-resistant polyol and curing agent. An intermediate layer, formed from an olefin-based acid copolymer ionomer composition and preferably an ethylene acid copolymer, is disposed between the rubber core and cover. The moisture-resistant polyol is preferably a reaction product of dimer acid or dimer ester and a polyolefin diol, or a polybutadiene polyol, or a polyisoprene. Preferably, the cover layer has a moisture vapor transmission rate (MVTR) between 3 grams·mm/m2·day to 4 grams·mm/m2·day.