In this work, we review, extend and discuss low-temperature specific-heat experiments, that we have conducted on different molecular (hydrogen-bonded) solids both in crystalline and glassy (either amorphous or orientationally disordered) phases. In particular, we have measured the low-temperature specific heat C-p for a set of simple, well known alcohols: glycerol, propanol and ethanol. For glycerol, we have prepared and measured C-p of both glass and crystal phases down to 0.5 K. The same has been done for propanol, in this case comparing the strikingly different values observed for the two chemical isomers, 1-propanol and 2-propanol. Moreover, ethanol exhibits a very interesting polymorphism presenting three different solid phases at low temperature: a fully ordered (monoclinic) crystal, an orientationally disordered (cubic) crystal or 'orientational glass' and the ordinary structural (amorphous) glass. By measuring and comparing the low-temperature specific heat of the three phases, in the boson peak range 2-10 K as well as in the tunnelling-state range below 1 K, we provide a quantitative confirmation that 'glassy behaviour', either concerning low-temperature properties or the glass-transition phenomenon itself, is not directly related to the lack of long-range crystalline order occurring in amorphous solids.