  We present a set of numerical experiments designed to systematically
investigate how turbulence and magnetic fields influence the morphology,
energetics, and dynamics of filaments produced in wind-cloud interactions. We
cover 3D magnetohydrodynamic systems of supersonic winds impacting clouds with
turbulent density, velocity, and magnetic fields. We find that log-normal
density distributions aid shock propagation through clouds, increasing their
velocity dispersion and producing filaments with expanded cross sections and
highly-magnetised knots and sub-filaments. In self-consistently turbulent
scenarios the ratio of filament to initial cloud magnetic energy densities is
~1. The effect of Gaussian velocity fields is bound to the turbulence Mach
number: Supersonic velocities trigger a rapid cloud expansion; subsonic
velocities only have a minor impact. The role of turbulent magnetic fields
depends on their tension and is similar to the effect of radiative losses: the
stronger the magnetic field or the softer the gas equation of state, the
greater the magnetic shielding at wind-filament interfaces and the suppression
of Kelvin-Helmholtz instabilities. Overall, we show that including turbulence
and magnetic fields is crucial to understanding cold gas entrainment in
multi-phase winds. While cloud porosity and supersonic turbulence enhance the
acceleration of clouds, magnetic shielding protects them from ablation and
causes Rayleigh-Taylor-driven sub-filamentation. Wind-swept clouds in turbulent
models reach distances ~15-20 times their core radius and acquire bulk speeds
~0.3-0.4 of the wind speed in one cloud-crushing time, which are three times
larger than in non-turbulent models. In all simulations the ratio of turbulent
magnetic to kinetic energy densities asymptotes at ~0.1-0.4, and convergence of
all relevant dynamical properties requires at least 64 cells per cloud radius.
