The application of electrodialysis for tartrate stabilization and reagent-free acidity correction of wine and juices is attracting increasing interest. New aliphatic membranes CJMC-3 and CJMA-3 and aromatic membranes CSE and ASE were tested to determine their suitability for use in these electrodialysis processes and to evaluate the fouling of these membranes by wine components for a short (6–8 h) operating time. Using IR spectroscopy, optical indication and measurement of surface contact angles, the chemical composition of the studied membranes, as well as some details about their fouling by wine components, was clarified. The current–voltage charsacteristics, conductivity and water-splitting capacity of the membranes before and after electrodialysis were analyzed. We found that in the case of cation-exchange membranes, complexes of anthocyanins with metal ions penetrate into the bulk (CJMC-3) or are localized on the surface (CSE), depending on the degree of crosslinking of the polymer matrix. Adsorption of wine components by the surface of anion-exchange membranes CJMA-3 and ASE causes an increase in water splitting. Despite fouling under identical conditions of electrodialysis, membrane pair CJMC-3 and CJMA-3 provided 18 ± 1 tartrate recovery with 31 · 10−3 energy consumption, whereas CSE and ASE provided 20 ± 1% tartrate recovery with an energy consumption of 28 · 10−3 Wh, in addition to reducing the conductivity of wine by 20 ± 1%. The casting of aliphatic polyelectrolyte films on the surface of aromatic membranes reduces fouling with a relatively small increase in energy consumption and approximately the same degree of tartrate recovery compared to pristine CSE and ASE.