This paper presents a measurement-based analysis of wideband 39 GHz millimeter wave (mm-wave) dual-polarized propagation channel under the impact of foliage presence between a transmitter (Tx) and a receiver (Rx). The measurements were conducted in a rich-vegetation area, and the so-called direction-scan-sounding (DSS) method which rotates a horn antenna in angular domains was applied, aiming at investigating the direction-of-arrival (DoA)-dependent characteristics of polarimetric channels. Four Tx-to-Rx polarization configurations were considered, including co-polarization scenarios with vertical Tx-polarization to vertical Rx-polarization (VV) and horizontal to horizontal (HH), as well as cross-polarization with vertical to horizontal (VH) and horizontal to vertical (HV), which allow scrutinizing the differences in delay-direction dispersion for usually-encountered scenarios. A foliage loss model for various vegetation depths in VV polarization configuration, was also presented in this paper. The results show that the foliage-loss DoA spectra for VH and HV are similar, while the spectra exhibit less penetration loss in most directions for VV than for the HH. Furthermore, the presence of vegetation between the Tx and the Rx leads to larger dispersion in delay compared to the clear line-of-sight (LoS) scenario, particularly for vertical polarization in the Tx side, and additionally, the foliage presence also results in evident DoA dispersion, specially in the HV scenario. Selectivity in directions caused by foliage is more significant in vertically-polarized Tx scenarios than in the horizontally-polarized Tx scenarios. A statistical model is established summarizing these comparison details.