Using ring polymer molecular dynamics simulations, we examine equilibrium and dynamical characteristics of solid-like, aqueous clusters that combine isotopic mixtures of HDO dilute in H₂O, at temperatures intermediate between 50 and 175 K. In particular, we focus attention on the relative thermodynamic stabilities of the two isotopes at dangling hydrogen bond sites. The water octamer is analyzed as a reference system. For this aggregate, decreasing temperature yields a gradual stabilization of the light isotope at dangling sites in molecules acting as single-donor-double-acceptors of hydrogen bonds. At T ~ 50 K, the imbalance between the corresponding quantum kinetic energies leads to a free energy difference between dangling and hydrogen bonded sites of the order of ~2k_BT. Similar free energy differences were found at dangling sites in N_w = 50 water clusters. The extent of the H/D segregation can be adequately monitored by modifications in the peak intensity of the high frequency shoulder of the stretching band of the infrared spectrum. These signals, in turn, represent a potential experimental signature of the elusive temperature of clusters in molecular beams.