Recent experimental results on positive charged formic acid clusters generated by the impact of Cf-252 fission fragments (FF) on icy formic acid target are examined in this paper by quantum mechanical calculations. Structures for the clusters series, (HCOOH)(n)H+ and (HCOOH)(n)H3O+, where 2 <= n <= 4, are proposed based on ab initio electronic structure methods. Results show that cluster growth does not present a regular pattern of nucleation. A stability analysis was performed considering the commonly defined stability function, where E is the total electronic energy plus the zero point vibrational energy correction, including the BSSE correction. The stability analysis leads to a picture that is compatible with experimental observations, indicating a decay of the stability with the increase of cluster mass. Temporal behavior of the clusters was evaluated by Born-Oppenheimer molecular dynamics to check the mechanism that provides cluster stability. The evaluated temporal profiles indicate the importance of hydrogen atom migration between the formic acid moieties to maintain the stability of the structures.