We present results of a hole-burning spectral diffusion experiment on a deuterated sample of horseradish peroxidase (substituted with free-base mesoporphyrin-IX) in a trehalose/glycerol glass. Like in earlier experiments, the spectral diffusion dynamics is well-described by a diffusion picture; the most noticeable observation is a power-law dependence of the hole-broadening on time. In addition, the comparison of the present data with our earlier experiments allows far a microscopic interpretation of the influence of trehalose on protein dynamics. Here, internal water molecules in the proteins seem to be of great importance.