I tried this recently, but it was a pond and it was still deep (in Canada, so part of it was frozen), and I lowered myself to the shore and jumped forward into the water. The second my body was submerged, I shot up and took a huge gasp. It's called the cold-shock response and it causes you to lose control of your body. I had to try not to thrash, but I couldn't help it. I didn't reach the point of getting frostbite or anything, but I could feel the heat leaving my body it's not painful in the way getting punched is, but it's extremely uncomfortable. If you manage to keep yourself from swimming to shore, you'll either pass out, go into cardiac arrest due to heart palpitations, or the gasping and lack of breath hold will make you feel weak or breathe water into your lungs.
I couldn't handle the feeling of being in 1 degree water with my muscles uncontrollably shaking, and my survival mode caused me to paddle back to shore within a couple of minutes.
To answer your question, yes it most definitely can be used to commit suicide, as there have been many intentional and unintentional deaths caused by cold water immersion. Is it a peaceful of comfortable way to die? Absolutely not and it's really difficult to force yourself to stay in the freezing water for more than a couple of minutes.