The changes in the spin depolarization length in zinc-blende semiconductors when an external component of correlated noise is added to a static driving electric field are analyzed for different values of field strength, noise amplitude and correlation time. Electron dynamics is simulated by a Monte Carlo procedure which takes into account all the possible scattering phenomena of the hot electrons in the medium and includes the evolution of spin polarization. Spin depolarization is studied by examining the decay of the initial spin polarization of the conduction electrons through the D'yakonov-Perel process, the only relevant relaxation mechanism in III-V crystals. Our results show that, for electric field amplitudes lower than the Gunn field, the dephasing length shortens with increasing noise intensity. Moreover, a nonmonotonic behavior of spin depolarization length with the noise correlation time is found, characterized by a maximum variation for values of noise correlation time comparable with the dephasing time. Instead, in high field conditions, we find that, critically depending on the noise correlation time, external fluctuations can positively affect the relaxation length. The influence of the inclusion of the electron-electron scattering mechanism is also shown and discussed.