Using computer simulations, the early stages of the adsorption of the CfAFP molecule to the ice surface were analyzed. We found that the ice and the protein interact at least as early as when the protein is about 1 nm away from the ice surface. These interactions are mediated by interfacial solvation water and are possible thanks to the structural ordering of the solvent. This ordering leads to positional preference of the protein relative to the ice crystal before the final attachment to the ice surface takes place, accompanied by the solidification of the interfacial water. It is possible because the solvation water of the ice-binding plane of CfAFP is susceptible to the overlapping with the solvation water of ice and is mostly changeable into ice itself. These remote interactions significantly increase efficacy of the adsorption process by facilitating the geometric adjustment of the active region of the CfAFP molecule to the ice surface. Because of the ordered nature of the water molecules at the ice-binding plane, the energy of their interactions with the ice-binding surface of the protein does not change upon the ongoing solidification of solvation water. However, the structure of the solvation water is not strictly ice-like and the growth of ice in the interfacial water is not initiated at the side of the protein. On the contrary, we find that solvation water of CfAFP solidifies slower than solvation water of ice - the solidification of interfacial water starts at the surface of ice. Moreover, in the presence of the CfAFP molecule, also solvation water of ice solidifies slower compared to the situation when the protein is not present next to the ice surface. Additionally, the presence of the protein molecule shifts the ratio of cubic to hexagonal ice that spontaneously forms at the ice surface, by introducing another layer of ordered water molecules - opposite to the ice lattice, at the other side of the crystallizing layer of water.