Phase-change is an essential and unavoidable process to obtain solid foam. We study experimentally the solidification dynamics of a model aqueous foam in contact with a cold substrate. The substrate temperature, the foam bubble radius and the liquid fraction are changed. We show that the freezing dynamics always starts by following a self-similar square root of time diffusive dynamics. These early dynamics are then predicted as a function of the control parameters using a 1D diffusion model and by treating our foam as a homogeneous fluid with equivalent thermophysical properties. In particular, we build a new expression for the foam conductivity. Finally, experimental and theoretical results are compared and interpreted. This study paves the way towards the understanding of the complex foam freezing dynamics at longer times, when the freezing is then coupled to water migration in the foam.