The turbulent component of the radiation scintillation index (b2t) for collimated laser beams is used to estimate the structure characteristic (С 2n ) of the air refractive index fluctuations in snowfalls. The b2t component is determined in finely disperse snowfalls from simultaneous measurements of the frequency spectrum and the scintillation index (b2). The structure characteristic С 2n is estimated using only those spectra, which included both the turbulent and hydrometeor maxima with a deep minimum between them. In snowfalls the structure characteristic С 2n decreases and does not exceed 4 10-15 cm-2/3. No regular interrelation has been found between С 2n and the volume scattering coefficient. The scintillation index b2 increases with the increasing divergence of a narrow laser beam. It does not exceed the maximum value possible in the turbulent atmosphere without precipitation. The probability distribution in a narrow divergent beam is not the lognormal distribution, but the gamma-distribution in the most cases. At low atmospheric turbidity, it is possible to reliably distinguish the haze and precipitation (rain) situations from the spectrum of radiation scattered near the focused beam and the wind velocity. The error of С 2n estimation, validity of the used assumptions, and the physical causes for the features observed are discussed.