I worked at a Data Recovery company for over 4 years. Freezing a hard drive is a common trick that can work, but only under very specific circumstances with very specific types of drive failure. However you have quite a few more "normal" things to try first.
First thing you need to do is isolate the problem. There's a possibility that you may just have a dying external enclosure. Take the drive out of it, and test it either internally or in another enclosure. It's possible the hard drive itself is fine. The fact that the light is flickering can mean the external enclosure is failing, since usually when drives start to fail and are not detected, either the light will not turn on, or be solid.
Once you get it up, you want to put the least amount of stress on it possible just in case. If it's detected by Windows or whatever OS have you, copy files off as soon as possible. And always make backups.
It is important to stress that external drives are made for backup and storage. It is NOT suggested to have one connected and on 24/7. If you need more internal space, install another internal hard drive because external cases do NOT offer proper ventilation to constantly running drives.
And please don't open the actual hard drive. I will cry if you do.