The behavior of the linear polarization parameters of UX Ori stars during their eclipses by circumstellar dust clouds is studied. A circumstellar disk with a disk wind creating a puffing in the dust sublimation zone is considered. We show that the disk puffing can strongly affect the degree of polarization and color index of the star during its eclipse. A strong wind can change the orientation of the plane of linear polarization. The scattered radiation from a thin disk is polarized perpendicularly to its plane, but the radiation from a disk with a strong wind can be polarized along the disk plane. A situation where the disk-scattered radiation is not polarized in a certain spectral band is possible owing to the disk puffing. There can be different orientations of the linear polarization of the disk radiation in different spectral bands.