I'm running a green white Commander deck and wanted to know if I could.
Alas, you may not. This is because, per the rules posted on mtgcommander.net,
The back face of a double-faced card is included when determining a card's colour identity.
So, while Loyal Cathar is a white card, a white spell on the stack, and a white creature on the battlefield (or a black creature when it's flipped), its Commander-specific color identity is actually white+black.