Interesting, but overcomplicated IMO. There is no point in having 2 snubbers to slow down the rise and fall time of current in the same circuit. All you really need to slow down the rise/fall time of the Peltier current is the inductor, plus a Schottky diode from the drain of the mosfet to +12V. Also missing from your circuit and absolutely essential is a good decoupling capacitor across the 12V supply.
See attached schematic for my suggestion. Keep the circuitry inside the dashed circle as compact as possible - that is the bit that will generate noise. L2 may not be needed, or a ferrite bead may suffice - its purpose is to persuade the switching current to take the path to ground through C1 instead of via the wires to the power supply. C1 needs to have a low ESR.
