Prediction of subgouge soil deformation during an ice gouging event is a challenging design factor in Arctic subsea pipelines. An accurate assessment of ice keel–seabed interaction requires expensive model testing and large deformation finite element analysis. Proposing reliable analytical/empirical solutions needs a deep understanding of the key parameters governing the problem. In this study, dimensional analysis of subgouge soil deformations was conducted and eight dimensionless groups of parameters were identified to facilitate proposing potential new solutions. A comprehensive dataset was established for horizontal and vertical subgouge deformations in both sand and clay seabed. Using the identified dimensionless groups, linear regression (LR) models were developed to estimate the horizontal and vertical deformation. Moreover, a sensitivity analysis (SA), as well as an uncertainty analysis (UA), was carried out to identify the superior LR models and the most influential parameter group. A high range of correlation coefficient (R), Nash-Sutcliffe efficiency coefficient (NSC), and variance accounted for (VAF) along with a low range of errors was achieved for the best LR model. The results of the superior LR models were also compared with the existing empirical equations. The study showed that the shear strength parameters of the seabed soil and the ratio of gouge depth to gouge width are the governing dimensionless parameters to model the horizontal and vertical subgouge soil deformations.