The photodissociation dynamics of HX (X = Cl, Br) molecules deposited on large ArN and (H2O)N, N̄ ≈ 10(2)-10(3), clusters is investigated at 193 nm using velocity map imaging of H and Cl photofragments. In addition, time-of-flight mass spectrometry after electron ionization complemented by pickup cross section measurements provide information about the composition and structure of the clusters. The hydrogen halides coagulate efficiently to generate smaller (HX)n clusters on ArN upon multiple pickup conditions. This implies a high mobility of HX molecules on argon. On the other hand, the molecules remain isolated on (H2O)N. The photodissociation on ArN leads to strong H-fragment caging manifested by the fragment intensity peaking sharply at zero kinetic energy. Some of the Cl-fragments from HCl photodissociation on ArN are also caged, while some of the fragments escape the cluster directly without losing their kinetic energy. The images of H-fragments from HX on (H2O)N also exhibit a strong central intensity, however, with a different kinetic energy distribution which originates from different processes: the HX acidic dissociation followed by H3O neutral hydronium radical formation after the UV excitation, and the slow H-fragments stem from subsequent decay of the H3O. The corresponding Cl-cofragment from the photoexcitation of the HCl·(H2O)N is trapped in the ice nanoparticle.