We investigate the tunneling magnetoresistance of small diameter semiconducting Si nanowires attached to ferromagnetic Fe electrodes, using first principles density functional theory combined with the non-equilibrium Green's functions method for quantum transport. Silicon nanowires represent an interesting platform for spin devices. They are compatible with mature silicon technology and their intrinsic electronic properties can be controlled by modifying the diameter and length. Here we systematically study the spin transport properties for neutral nanowires and both n and p doping conditions. We find a substantial low bias magnetoresistance for the neutral case, which halves for an applied voltage of about 0.35 V and persists up to 1 V. Doping in general decreases the magnetoresistance, as soon as the conductance is no longer dominated by tunneling.