The paper presents some results of statistical processing of experimental data on the backscattering phase matrices (BSPMs) of the ice crystal clouds. Using a sample of 463 matrices, we have determined the relative frequencies of elements of normalized reduced BSPMs, the parameter characterizing the degree of orientation preference of cloud particles about some azimuth direction Ф0, and the frequencies of occurrence of that or other Ф0 values. The term reduced BSPM is taken to emphasize that the matrix is defined in the coordinate system whose reference plane xOz coincides with the direction Ф0. Thus, the BSPMs turn out to be expressed through parameters independent of random Ф0 values, so that all BSPMs can be compared. It is concluded that in almost all situations observed, the particles have more or less preferred orientations about certain azimuth direction and about the horizontal plane. The particle orientation is nearly random in 70% of cases, and has essentially pronounced preferred direction in the other cases. It is suggested that the preferred particle orientation along some azimuth direction may be due to wind velocity variations. Generally, the particles are oriented with their long axis perpendicular to the wind velocity vector, i.e., normal to the Ф0 direction.