Cosmic dust models are key ingredients in advancing our understanding of astronomical environments as diverse as interstellar clouds in galaxies, circumstellar envelopes around evolved and young stars, and protoplanetary disks. Such models consist of several dust populations, each with different compositions and size distributions. They may also consider different grain shapes, although most models assume spherical grains. All include a component of silicate dust. The absorption and emission properties of these dust components are calculated from the optical constants of each dust material which have various experimental, phenomenological, and theoretical origins depending on the model. We aim to provide the community with new sets of optical constants for amorphous silicate dust analogues at low temperatures. The analogues consist of four Mg-rich silicate samples of stoichiometry ranging from enstatite to olivine, and of eight samples of Mg and Fe rich silicates with a pyroxene stoichiometry and differing magnesium and iron content. We calculated the optical constants from transmission measurements using the Kramers-Kronig relations, assuming that the grains are small compared to the wavelength and prolate in shape with axis ratios of 1.5 and 2 for the Mg and Fe rich samples, respectively. New optical constants for silicate dust analogues were calculated over the wavelength range from 5 to 800-1000 microns, depending on the sample, and at temperatures of 10, 30, 100, 200, and 300 K.We determined the uncertainties on the derived optical constants based on the assumptions used to calculate them. To facilitate the use of these data in cosmic dust models, we provide optical constants extrapolated outside the measured spectral range into the UV-NIR and mm-cm wavelength ranges, as well as formulae that can be used to interpolate them at any temperature in the range 10 - 300 K.