Tempranillo red wines were partially dealcoholized (−3 v/v%) by osmotic distillation (OD) with membranes. First, polypropylene (PP) Liqui-Cel3M (3M) hollow fiber membrane modules were applied at 11 and 15 °C to study the effect of the removal of ethanol on the aroma of a certain wine. The influence of both temperatures was evaluated in terms of ethanol flux and aroma losses. Afterwards, two additional wines with different compositions were dealcoholized. The impact of the initial concentration of aromas on achieving a final product with an appealing aroma profile was studied, displaying the three wines a comparable aroma retention. Membrane OD was carried out with two additional hollow fiber membrane modules: another PP module (Zena) with a higher pore size, and a superhydrophobic PVDF module (Polymem). The latter gave rise to a partial dealcoholized wine with an aroma profile very similar to that of the pristine wine.