I play Morrowind on my 360, and would like to know if there is any way to toggle the crouch/sneak mode. Also, I read that there is supposed to be some sort of "sneak icon," or is that information wrong?

To toggle sneak on and off, you need to click the left thumbstick. It can be kind of tricky and took me a few tries to get it to actually stay. Try holding it down to sneak, and quickly click it. As for the icon, it's a little symbol by your selected weapon/spell at the bottom left, not in the middle of the screen as it is in Oblivion.

Edit: Spelling/Grammar

And it only appears if your are not being detected.

Apparently you need to click the left thumbstick twice, really fast. I've never bothered myself. Stealth sux.