We investigate the interaction of colloidal particles with the ice-water interface using a combination of a directional solidification stage, a light microscope and thin sample cells. Firstly, we focus on separating the contributions of colloids from that of salt in inducing the Mullins- Sekerka instability of the ice-water interface. We show that while the instabilities more quickly develop at higher freezing velocities, the presence of the particles enhances the development of the perturbations. Consequently, we observe fully developed instabilities as 'ice-fingers' only when particles are present and at high freezing velocities. Secondly, we study the structures formed by the colloidal particles accumulating in front of the ice-water interface during the unidirectional freezing. By using di↵erent image analysis methods, we find that despite the slow freezing velocity, the increase of the particle concentration in front of the interface is still too quick for the formation of a crystal structure. However, once the particles have been entrapped by the ice, they form linear or zig-zag structures between the ice fingers. Thirdly, we look at the event of 'thermal regelation', specifically the movement of single particles in ice towards the ice-water interface. This is possible due to the presence of a premelted liquid film, surrounding the particle. Particle movement is measured by using tracking algorithms, and fitted to theoretical predictions, which capture a thermomolecular and a viscous force to describe the motion. From this we are able to determine that non-retarded van der Waals interactions dominate this premelting for our particle-ice system. In the last chapter, we study the 3D shape of the interface, and show how it is curved between the two walls. An earlier theory describing the typical curvature is shown not to work, and by varying material properties, we show that thermal conductivities of the different materials likely need to be accounted for. We finish the thesis with a conclusion and outlook.