The coherent spin dynamics of holes are investigated for CsPbBr3 and CsPb(Cl,Br)3 perovskite nanocrystals in a glass matrix using the time-resolved Faraday rotation/ellipticity techniques. In an external magnetic field, pronounced Larmor spin precession of the hole spins is detected across a wide temperature range from 5 to 300 K. The hole Landé g-factor varies in the range of 0.8-1.5, in which it increases with increasing optical transition energy due to enhanced confinement in small nanocrystals. The hole spin dephasing time decreases from 1 ns to 50 ps in this temperature range. Nuclear spin fluctuations have a pronounced impact on the hole spin dynamics. The hyperfine interaction of the holes with nuclear spins modifies their spin polarization decay and induces their spin precession in zero external magnetic field. The results can be well described by the model developed in [I. A. Merkulov, Phys. Rev. B 65, 205309 (2002)0163-182910.1103/PhysRevB.65.205309], from which the hyperfine interaction energy of a hole spin with the nuclear spin fluctuation in the range of 2-5μeV is evaluated.