Honestly I have not found a way to this problem of Windows 7 freezing while watching YouTube but I have solution to overcome without hard resetting your computer.
I too face this most irritating issue while watching YouTube; all I did was hard resetting my computer and obviously I loose all my working files. I searched the whole Google Search Engine, tried different browser, updated flash player but still no luck. After so many days, I simply tried the method of ‘Switch User’ option in Windows 7 and it really worked!!!
No need to login with another user account. You try to login with the same user account that is currently hanged. You won’t believe, it works! you can access all your current opened windows and the hanged streaming YouTube video will work this time.