There are numerous indications that the Milky Way has a hot material outflow originating from the Galactic center. Among others, the so-called Fermi bubbles discovered in 2010 strengthens this possibility. The origin of this nuclear wind is still disputed, either the episodic activity of Sagittarius A$^*$, the supermassive black hole at the Galactic center, or a nuclear start burst in its vicinity have been invoked as possible powering sources. In any case, these symmetrical structures, already observed in both gamma-rays, X-rays, and radio, show evidence of a hot magnetized coronal phase entrained by molecular clouds. Moreover, radio polarization measurements evidence the presence of structured magnetic fields in the general perpendicular direction to the central Galactic plane. Indeed, magnetohydrodynamic simulations point to the possible existence of a well-structured field reaching as high as 15 kpc or more above the energy input region in the plane, with intensities on the order of tens of $\mu$G. This field can be blown over the plane and twisted azimuthally due to the angular momentum conservation, to form an extended magnetized Halo. Using a simple model of such a magnetic field structure, we assess the possible impact of this environment on the interpretation of the arrival directions of incoming Ultra-High energy cosmic rays as a function of rigidity.