MBP Freeze + Graphics Card Problems
I ran into a similar issue a while back.  You will need to diagnose the video card with a diagnostic utility

1)  Download, burn, and boot Ultimate Boot CD.  There are a number of video utilities you can run that will test out your video card for you.  Since you are no longer booting OS X when you boot this CD, you are bypassing any software issues you may be experiencing from Apple and OS X.  

There is a USB Flash Boot Drive option instead of a CD (I personally use this). 

This will tell you if your video chip is good or bad.  If it fails at any point, then it is a safe bet that you have a hardware issue.  If everything passes, it's on to step 2.

2) Install a pervious version of OS X; Mavericks or Mountain Lion will do.  The best way is to boot from a USB drive (don't overwrite the HDD in your MBP).  A small USB drive is fine 10/20 GB is more than enough.  This is just to install OS X 10.9.x or 10.8.x so you can do some diagnostics.

Do a Time Machine Backup First!  Just in case you accidentally select the internal drive when doing this procedure.

Do a fresh install of ML or Mavericks on the USB HDD.  Let it wipe and partition the drive.  

3)  Boot from the USB HDD (hold down the option key before the boot chime to select boot device).  Install Chrome and watch videos as you normally would.  If everything works properly, you have narrowed down the problem to Yosemite.    Which means you will probably have to wait for a fix from the folks at Apple.

At that point, you have really only two options:  downgrade to Mountain Lion or Mavericks or wait for an update to Yosemite.