I agree with everyone here...

I was in Banff (at the Fairmont) from 28 Dec 08 to 01 Jan 09 and had no problems any of those days to get street parking on the road leading to & away from the hotel. As other noted, you park as you are leaving away from the hotel.

In addition, I had no problem parking in downtown Calgary on the weekend, and although I didn't stay at a Fairmont (I did Westin), it should be about the same...as long as you don't mind walking a few blocks. That said, I walked at the end of December - so the walk wasn't the most pleasant...but it was well worth saving ~$20 a night!

-jeremy