TL;DR No, this is a terrible idea.
Cutting a hole into a fridge, and hooking up a line to it that goes to your PC will not achieve the results you are looking for. The line will cause condensation to build up inside of your computer, and ruin it over time. It is also not very efficient for cooling.
A refrigerator will actually slightly raise the ambient temperature of the room. On hotter days, it will put out even more heat because the compressor has to work harder.
What you really should do is lower the ambient temperature of the room. You want to aim for a temperature that is below 80 degrees Fahrenheit. There will be a significant increased risk of component failure if it gets much higher.
An air conditioner is the cheapest alternative to lowering the temperature of the room. If you do not have one, and cannot put one in that space, then it would be a good idea to locate your computer in a different room that is cooler on average.
Water cooling is almost never necessary. They are most often used in overclocked computers. Usually, the stock fans that comes with a system are good enough. Usually, when people are complaining about overheating issues, they are either overclocking, or their PC is full of dust. If you are overclocking, put all of the settings back to default to see if that helps the stability issues. You should also spray out our machine thoroughly with compressed air, especially around the fans.
Some PCs do not have very good airflow. You can try adding or replacing fans to see if that makes a difference. Fans wear out over time, and can become less efficient.