The theory of radiatively driven winds successfully explains the key points of the stellar winds of hot massive stars. However, there is an apparent break-down of this paradigm at log L/L_&odot <5.2: the stellar wind momentum is smaller than predicted for low luminosity early-type stars from metal poor environments, and there are also some Galactic examples. We present a preliminary analysis of a small sample of stars of this luminosity regime in the Orion Nebula region and evaluate whether magnetic fields may play some role in the weak wind problem.