We have sequentially picked up two astrochemically relevant Bronsted acids (methanol and formic acid) on the surface of argon nanoparticles acting as a cold support. Photoionization and electron ionization yield (HCOOH)(x)H+, (CH3OH)(x)H+, and mixed protonated clusters. Experiments with perdeuterated methanol CD3OD demonstrate notable proton transfer (PT) to formic acid acting as a proton acceptor in addition to the PT from formic acid which is, perhaps, a more intuitive one. We, therefore, for the first time observed reactions between two different complex molecules adsorbed individually on argon nanoparticles. The experimental results are compared with state-of-the-art quantum chemistry calculations, showing that both CH3OH center dot+ and HCOOH center dot+ radical cations resulting from ionization can act as efficient proton donors and neutral CH3OH and HCOOH as proton acceptors. According to the theoretical calculations, the C-H bond cleavage in the radical cation should be more favorable than the O-H bond cleavage. Both channels are observed and distinguished in the experiments with CD3OH and CH3OD. Our detailed mechanism of formation of the CH3O center dot and CH2OH center dot radicals contributes to understanding of astrochemistry in the protostellar medium.