The linear equations for transverse spin dynamics in a weakly polarized degenerate Fermi liquid with arbitrary relationship between temperature T and polarization γH are derived from LandauSilin phenomenological kinetic equation with general form of two-particle collision integral. The temperature and polarization dependence of the spin current relaxation time is established. It is found in particular that at finite polarization transverse spin wave damping has a finite value at T = 0.The analogy between temperature dependences of spin waves attenuation and ultrasound absorption in degenerate Fermi liquid at arbitrary temperature is presented.We also discuss spin-polarized Fermi liquid in the general context of the Fermi-liquid theory and compare it with "Fermi liquid" with spontaneous magnetization.