Here is a cougar track with a coyote track just behind and beside it in snow. The cougar stepped on its own track so it shows an extra toe from the track below.
Cougar tracks rarely show any claw, but if they are running, scrambling up a steep bank, etc. they might dig in a claw to where it might show, or in deeper mud a claw might show a bit. The three lobes across the back say cat. The coyote track is not as clear but the claws showing at the front say canine immediately when combined with the over all shape, arrangment of toes and pad shape.
I'd really like to see a photo of the track you saw, so post it if you can. Open a Photobucket account, post the photo there and then copy the IMG code under it and paste that in a post here. E-mail it to me if nothing else works. Send me a private message (PM) if you want to go that way.
Here are a couple of cougar paws showing the distinctive shape that makes the distinctive tracks.