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This paper presents the results of an experimental study of the reaction of OH^– anions with HD molecules leading to the formation of OD^– anions. The study's main goal was to obtain the temperature dependence of the reaction rate coefficient and determine the reaction's enthalpy. This study was carried out at astrophysically relevant temperatures from 15 to 300 K. The reaction was studied using a temperature-variable cryogenic linear 22-pole radio-frequency ion trap. The rotational temperature of the OH^– anions in the ion trap was characterized by near-threshold photodetachment spectroscopy. At 15 K, the measured reaction rate coefficient is 5 × 10^–10 cm³ s^–1. With increasing temperature, the reaction rate coefficient decreases monotonically to 5 × 10^–11 cm³ s^–1 at 300 K. Comparing with the previously determined rate coefficient of the reverse reaction of OD^– anions with H₂, we obtained the temperature dependence of the equilibrium constant. The enthalpy and entropy of the title reaction were determined in the studied temperature range as ΔH = (-23.9 ± 0.7 ± 2.6^sys) meV and ΔS = (-8.5 ± 1.2 ± 1.4^sys) J mol^–1 K^–1, respectively.