At terahertz frequencies, the libration-vibration motions couple to the dielectric relaxations in disordered hydrogen-bonded solids. The interplay between these processes is still poorly understood, in particular at temperatures below the glass transition temperature, Tg, yet this behavior is of vital importance for the molecular mobility of such materials to remain in the amorphous phase. A series of polyhydric alcohols were studied at temperatures between 80 and 310 K in the frequency range of 0.2-3 THz using terahertz time-domain spectroscopy. Three universal features were observed in the dielectric losses, ϵ″(ν): (a) At temperatures well below the glass transition, ϵ″(ν) comprises a temperature-independent microscopic peak, which persists into the liquid phase and which is identified as being due to librational/torsional modes. For 0.65 Tg < T < Tg, additional thermally dependent contributions are observed, and we found strong evidence for its relation to the Johari-Goldstein secondary β-relaxation process. (b) Clear spectroscopic evidence is found for a secondary β glass transition at 0.65 Tg, which is not related to the fragility of the glasses. (c) At temperatures above Tg, the losses become dominated by primary α-relaxation processes. Our results show that the thermal changes in the losses seem to be underpinned by a universal change in the hydrogen bonding structure of the samples.