EM noise from Peltier cooler
The peltier won't produce electromagnetic noise necessarily but the PWM will, which at a closest approximation is like a square wave. Ttherfore the fundamental frequency of the square wave will determine most noise that you see and it can show up in many places, even analog electronics.
The EM noise will be both RF and magnetic, RF from capacitance between the cable\peliter and everything else. Magnetic from the current.
If you do run PWM, you'll need to have proper shielding techniques (shielded cable, ferrites, ect). In addition, the PWM noise can be conducted because of the power being switched and bleed into analog electronics if they are on the same supply.
I have built both types of systems (PWM and voltage controlled peliters) I would suggest to leave the headache out of it if you can and run a voltage controlled scheme with a high current amplifier and a DAC (sometimes higher powers above 2A can be hard to achieve with voltage controlled peliters and only PWM will suffice). A voltage controlled scheme should be used if the power is in the 100mA range and you have sensitive electronics.