In WRF, we produce met_em* files at several times, but in the common case, the first met_em file is used to produce the model initial conditions, and subsequent met_em files are only used to produce lateral boundary conditions. The full fields from met_em files are not used to update the model state in the interior of the model domain during the course of a WRF simulation.
As a matter of clarification, when you say "every time step", are you referring to the interval between, e.g., met_em files in WRF? I think most WRF and MPAS-Atmosphere users would take the term "time step" to refer to the Runge-Kutta time steps used in the model numerical integration of the equations of motion, which is not the same as, e.g., the interval between lateral boundary updates in WRF. For typical model grids/meshes used in WRF and MPAS-Atmosphere applications, the numerical integration timestep may be on the order of one minute (perhaps between 18 s and 720 s for 3-km meshes out to 120-km meshes).
Could you clarify when exactly you need to read the updated theta_m field in the context of the above? You can have the MPAS-Atmosphere model write restart files and stop as frequently as you would like. At each of these restart times, you could modify the theta_m and other fields, then restart the model with the updated theta_m to integrate for another time period. Alternatively, could you clarify whether you want to truly overwrite the model theta_m field, or to just add tendency (nudging) terms to the field during the numerical integration in the model?
I think it might help if I better understood your end goal with these experiments. Are you trying to implement some sort of cycled data-assimilation, or to estimate error growth rates in the model, or something else?