Why is the body cooled during cardiac surgery?
As you mention, hypothermia is routinely induced during cardiac surgery. There is a blog post including a photo of a heart being cooled with ice chips here: https://www.heart-valve-surgery.com/heart-surgery-blog/2010/10/17/ice-cardioplegia-open-heart-surgery/



The primary therapeutic benefit of deliberate hypothermia was long thought to be, as you say, the slowing-down metabolic processes, which reduces the amount of oxygen needed by the brain and other vital organs (source). Cooling the blood during open heart surgery therefore allows the operation to be performed more slowly (2-4 hours).

However, according to this open-access article on the benefits of therapeutic hypothermia for cardiac surgery:


  the widely held notion that hypothermia protects because lower
  temperatures slow metabolism is not completely accurate. Recent
  research has shown that hypothermia can alter a plethora of cell death
  and cell survival pathways including gene regulation resulting in the
  inhibition of apoptosis and inflammation and the up-regulation of
  anti-apoptotic or trophic factors.


So basically it does slow down the metabolic processes but it also reduces inflammation and cell death.

After surgery, rewarming needs to be done slowly to maximise the chances of recovery (source).