The present work focuses on the study of magneto-hydrodynamic phenomena in inductively coupled plasma (ICP) wind tunnels. To this purpose a versatile multi-physics framework has been developed, where a fluid solver is coupled with an electro-magnetic solver. The flow governing equations are discretized in space based on a cell-centered finite volume method. A preconditioned compressible formulation is adopted to tackle the stiffness resulting from low Mach numbers occurring in ICPs. Electromagnetic equations are solved in a mixed finite-element solver, where H(curl) and H(Div) conforming finite element spaces are used for the electric and magnetic fields, respectively. Results are obtained for 2D-axisymmetric ICP configurations under both LTE and NLTE conditions. Time accurate simulations with high order schemes are also performed to capture the transient flow features often observed in actual plasmatron facilities and study its effect on the material ablative properties.