We study the wetting of polymer layers by polar solvents. As previously observed, when a droplet of solvent spreads, both its contact angle and velocity decrease with time as a result of solvent transfers from the droplet to the substrate. We show that, when the polymer is initially glassy, the angle decreases steeply for a given value of the velocity, Ug. We demonstrate that those variations result from a plasticization, i.e., a glass transition, undergone by the polymer layer during spreading, owing to the increase of its solvent content. By analyzing previous predictions on the wetting of rigid and soft viscoelastic substrates, we relate Ug to the viscosity of the polymer gel close to the glass transition. Finally, we derive an analytical prediction for Ug based on existing predictions for the water transfer from the droplet to the substrate. Using polar solvents of different natures, we show that the experimental data compare well to the predicted expression for Ug.