A novel cryostat was developed for in situ neutron scattering studies on vapor-deposited amorphous samples. By the use of this cryostat, vapor-deposited amorphous ice was prepared at ca. 8 K. The neutron scattering spectra of the as-deposited sample and those annealed at ca. 120 K, 160 K, and 250 K were measured at 50 K in energy range below 100 meV. The four samples studied corresponded to vapor-deposited amorphous solid water (ASW), hyperquenched glassy water (HGW) (approximately), ice I-c, and ice I-h, respectively (according to historical nomenclature). The librational frequency of the water molecule is smaller in the order of ASWHGW>ASW. The absolute value of the vibrational density of states G(E) was obtained from the analysis combining the heat capacity and neutron scattering data. G(E) of ASW and HGW integrated below 6 meV were larger than that of ice I-h(approximate toI(c)) by 0.060 and 0.039 degrees of freedom per water molecule, respectively. Similar experiments were performed on the vapor-deposited amorphous ice doped with 5% and 10% of methanol (CD3OH). The magnitude of G(E) below 6 meV increased with increasing fraction of methanol. All of the results in this study indicate that the low energy excitation [G(E) below 6 meV] of amorphous ice is enhanced by the defects and distortion of the hydrogen bonds.