Photodetachment thermometry on a beam of OH^{-} in a cryogenic storage ring cooled to below 10 K is carried out using two-dimensional frequency- and time-dependent photodetachment spectroscopy over 20 min of ion storage. In equilibrium with the low-level blackbody field, we find an effective radiative temperature near 15 K with about 90% of all ions in the rotational ground state. We measure the J=1 natural lifetime (about 193 s) and determine the OH^{-} rotational transition dipole moment with 1.5% uncertainty. We also measure rotationally dependent relative near-threshold photodetachment cross sections for photodetachment thermometry.