Hold down on the sleep button and the home button at the same time for about 10 seconds until the Apple logo appears on the screen, let go of the buttons and the iPad should restart. If Safari continues to freeze after you restart, try this.
Tap Settings, then tap Safari on the left side. Then on the right side - tap clear history, clear cookies, clear cache. Clear all three. Reboot your iPad. Hold down on the sleep button at the top until the red slider appears and slide to power off. Then hold down on the sleep button until the Apple logo appears and the iPad will restart. Launch Safari and see if helped.
Message was edited by: Demo
If the YouTube app freezes entirely - meaning that the controls will not work - you get no response from the play button or the done button - this might work for you.
You could try quitting open apps to see if that helps. Double tap the home button to bring up the task bar, hold down on any app icon until the icons begin to wiggle. Tap the minus sign in the corner of the icons to close the apps. If you have a bunch of apps in the task bar, close them all. Then tap the screen (outside of the task bar) to close the task bar. Restart the iPad. Hold down on the sleep button until the red slider appears and slide to turn off. Hold down on the sleep button until the Apple logo appears to restart.
If the videos in YouTube will start and then stop while you are playing them, but you can start them again successfully, that sounds more like a slow Internet connection causing the videos to not load fast enough.
This worked for me (found it totally by accident but it worked):
1. Power on, click on the SETTINGS icon
2. click on Safari
3. Change search engine preferences (it was on Google, I switched to Yahoo)
4. Press the power button to return to the icon screen
5. activate Safari.
This process cleared up the frozen grey Safari screen for me. Hope it works for you.