Peltier wiring diagram
Is it possible to power the peltier with a motor speed controller
  220vac input and variable output. If no, why?


Sure it's possible, is it safe? No. 

Does the above circuit risk electrocution? If the motor controller does not have galvanic isolation, then yes. 

The other problem is the output of the controller shows 220V, which is above the 48V rating of the peltier modules and is sure to exceed the maximum ratings and burn them up. 

Find a DC power supply with voltage control at minimum. Also running peliters at full power can be bad because the heating from resistive losses in the peliters causes them to heat up and gives you less cooling