This paper is dedicated to the solidification of a water drop impacting a cold solid surface. In the first part, we establish a one-dimensional (1-D) solidification model, derived from the Stefan problem, that aims at predicting the freezing dynamics of a liquid on a cold substrate, taking into account the thermal properties of this substrate. This model is then experimentally validated through a 1-D solidification set-up, using different liquids and substrates. In the second part, we show that during the actual drop spreading, a thin layer of ice develops between the water and the substrate and pins the contact line at its edge when the drop reaches its maximal diameter. The liquid film then remains still on the ice and keeps freezing. This configuration lasts until the contact line eventually unpins and the liquid film retracts on the ice. We measure and interpret this crucial time of freezing during which the main ice layer is built. Finally, we compare our 1-D model prediction to the thickness of this ice pancake and we find a very good agreement. This allows us to provide a general expression for the frozen drop’s main thickness, using the drop’s impact and liquid parameters.