The physics and modelling of cooling and freezing of droplets in contact with a colder substrate are of interest in various engineering applications. This work provides experimental results of this process employing infrared thermography for temperature measurements at the droplet´s surface. Also, a high-speed camera is employed to observe the recalescence period and measure the freezing front movement and the droplet shape change. Three substrates are prepared with distinct wettability ranges, i.e. one hydrophilic and two hydrophobic surfaces. From the experimental observation of a solidification front parallel to the substrate plane, a mixed lumped-differential model of the heat transfer process based on the Coupled Integral Equations Approach (CEIA) is proposed, reformulating the two-dimensional partial differential formulation in cylindrical coordinates into a one-dimensional transient energy equation for the droplet external surface temperature. Direct comparisons of the experimental and theoretical results for the supercooling period show excellent agreement for the droplet surface temperatures at different heights and for different values of the substrate-droplet contact angle.The file "figures 7&8.xlsx" contains the temperature of three locations along the droplet axis as recorded using IR camera, during the droplet's cooling and freezing. The IR data presented here is downsampled. The file "figure 10.xlsx" contains the freezing front position during the droplet's freezing, captured using high speed shadowgraph technique.