Resonance properties of nanomechanical resonators based on doubly clamped silicon nanowires, fabricated from silicon-on-insulator and coated with a thin layer of aluminum, were experimentally investigated. Resonance frequencies of the fundamental mode were measured at a temperature of $20\,\mathrm{mK}$ for nanowires of various sizes using the magnetomotive scheme. The measured values of the resonance frequency agree with the estimates obtained from the Euler-Bernoulli theory. The measured internal quality factor of the $5\,\mathrm{\mu m}$-long resonator, $3.62\times10^4$, exceeds the corresponding values of similar resonators investigated at higher temperatures. The structures presented can be used as mass sensors with an expected sensitivity $\sim 6 \times 10^{-20}\,\mathrm{g}\,\mathrm{Hz}^{-1/2}$.