Binaries with hot massive components are strong X-ray sources. Besides the intrinsic X-ray emission of individual binary members originating in their winds, X-ray emission stems from the accretion on the compact companion or from wind collision. Since hot star winds are driven by the light absorption in the lines of heavier elements, wind acceleration is sensitive to the ionization state. Therefore, the over-ionization induced by external X-ray source strongly influences the winds of individual components. We studied the effect of external X-ray irradiation on hot star winds. We used our kinetic equilibrium (NLTE) wind models to estimate the influence of external X-ray ionization for different X-ray luminosities and source distances. The models are calculated for parameters typical of O stars. The influence of X-rays is given by the X-ray luminosity, by the optical depth between a given point and the X-ray source, and by a distance to the X-ray source. Therefore, the results can be interpreted in the diagrams of X-ray luminosity vs.~the optical depth parameter. X-rays are negligible in binaries with low X-ray luminosities or at large distances from the X-ray source. The influence of X-rays is stronger for higher X-ray luminosities and in closer proximity of the X-ray source. There is a forbidden area with high X-ray luminosities and low optical depth parameters, where the X-ray ionization leads to wind inhibition. There is excellent agreement between the positions of observed stars in these diagrams and our predictions. All wind-powered high-mass X-ray binary (HMXB) primaries lie outside the forbidden area. Many of them lie close to the border of the forbidden area, indicating that their X-ray luminosities are self-regulated. We discuss the implications of our work for other binary types.