The Galactic halo contains a complex ecosystem of multiphase intermediate-velocity and high-velocity gas clouds whose origin has defied clear explanation . They are generally believed to be involved in a Galaxy-wide recycling process , either through an accretion flow or a large-scale fountain flow , or both . We examine the evolution of these clouds in light of recent claims that they may trigger condensation of gas from the Galactic corona as they move through it . We measure condensation along a cloud ’ s wake , with and without the presence of an ambient magnetic field , using two- ( 2D ) and three-dimensional ( 3D ) , high-resolution simulations . We find that 3D simulations are essential to correctly capture the condensation in all cases . Magnetic fields significantly inhibit condensation in the wake of clouds at t \gtrsim 25 Myr , preventing the sharp upturn in cold gas mass seen in previous non-magnetic studies . The magnetic field suppresses the Kelvin-Helmholtz instability responsible for the ablation and consequent mixing of a cloud with halo gas which drives the condensation . This effect is universal across different cloud properties ( density , metallicity , velocity ) and magnetic field properties ( strength and orientation ) . Simple convergence tests demonstrate that resolving the gas on progressively smaller scales leads to even less condensation . While condensation still occurs in all cases , our results show that an ambient magnetic field drastically lowers the efficiency of fountain-driven accretion and likely also accretion from condensation around high-velocity clouds . These lower specific accretion rates are in better agreement with observational constraints compared to 3D , non-magnetic simulations .