Using molecular simulation, we shed light on the crystal nucleation process in systems of Cu, Ni, and their nanoalloy. For each system, we simulate the formation of the crystal nucleus along the entire nucleation pathway and determine the free energy barrier overcome by the system to form a critical nucleus. Comparing the results obtained for the pure metals to those for the nanoalloy, we analyze the impact of alloying on the free energy of nucleation, as well as on the size and structure of the crystal nucleus. Specifically, we relate the greater free energy of nucleation, and bigger critical nuclei, obtained for the nanoalloy, to the difference in size and cohesive energy between the two metals. Furthermore, we characterize the dependence of the local composition of the incipient crystal cluster on its size, which is of key significance for the applications of bimetallic nanoparticles in catalysis.