Context. Planets and their atmospheres are built from gas and solid material in protoplanetary disks. Recent results suggest that solid material such as pebbles may contribute significantly to building up planetary atmospheres. In order to link observed exoplanet atmospheres and their compositions to their formation histories, it is important to understand how icy pebbles may change their composition when they drift radially inwards in disks. Aims. Our goal is to model the compositional evolution of ices on pebbles as they drift in disks, and track how their chemical evolution en route changes the ice composition relative to the ice composition of the pebbles in the region where they grew from micron-sized grains. Methods. A state-of-the-art chemical kinetics code was utilised for modelling chemical evolution. This code accounts for the time-evolving sizes of the solids that drift. Chemical evolution was modelled locally for 0.1 Myr at two starting radii, with the micron-sized solids growing into pebbles simultaneously. The pebbles and local gas, isolated as a parcel, were then exposed to changing physical conditions, which was intended to mimic the pebbles drifting inwards in the disk midplane, moving to 1 AU on three different timescales. A modelling simplification was that the pebbles are not moved through, or exposed to new gas, but they stayed in the same chemical gas surroundings in all models. Results. For ice species with initial abundances relative to hydrogen of >10-5, such as H2O, CO2, CH3OH, and NH3, the abundances change by less than 20% for both radii of origin, and for the two smaller drift timescales (10kyr and 100 kyr). For less abundant ice species, and the longest drift timescale (1 Myr), the changes are larger. Pebble drift chemistry generally increases the ice abundances of CO2, HCN, and SO, at the expense of decreasing the abundances of other volatile molecules.