Using ATI and Nvidia Cards together I want to mine Litecoin on an ATI 7950 while being able to play on my GTX 680.

Is this possible ? If yes then how ?
Your issue is trying to run ATI and Nvidia video drivers at the same time.

Many people mine on Linux LiveUSB.

This would be different if
a second GPU was so that you could get both of them to mine litecoin at the same time.In that case you would want your GTX680 not only mine but also display, where your other ATI card would do nothing but mining. 

This I haven't tried personally but people have using plug and play 

The system begins with the graphic card in the PCI-E closest to the CPU, all drivers were installed for Nvidia first

Put 7950 in the machine

Windows will ask to restart the system, I guess to figure out that it's had a hardware change, so restart

Install AMD drivers

For Windows to see the card, plug it into another monitor. Another way is too use a dummy plug: http://www.overclock.net/t/384733/the-30-second-dummy-plug