This paper focuses on the hydrogenation process in metal-polymer complexes based on copolymers of polypropylene glycol fumarate phthalate and polypropylene glycol maleate phthalate, using acrylic acid and immobilized cobalt metal particles as catalysts. A classical reaction of the electrocatalytic hydrogenation of pyridine to piperidine was applied. SEM and dynamic light scattering were utilized to investigate the average size and dispersity of cobalt metal nanoparticles. The experimental findings show that the efficiency of hydrogenation can be improved by increasing the temperature from 25 to 40 °C and the current to 2 A. More specifically, increasing the temperature to 40 °C promotes swelling of the polymer and its transition from a globular collapsed state to an open one, which leads to an increase in the number of active catalytic centers and, as a consequence, acceleration of the hydrogenation process. Increasing the current strength to 2 A also helps to increase the rate of the hydrogenation process. Further increasing the current to 3 A is undesirable due to an increase in the yield of by-products and a decrease in the yield of the target product, piperidine. Based on a comparative analysis, it was established that the use of a copolymer of polypropylene glycol maleate phthalate with acrylic acid as the polymer matrix base is the most preferable for obtaining polymer-metal complexes with nanosized cobalt.