Hey Susan, There are a few companies and most of them have a good reputation. Personally I can vouch for Brewster Adventures.
I went horseback riding with them on the last day of summer last year and it was definitely one of the highlights of my trip to the Rockies.
It is a very friendly and professional business and the stable seems really well run. The horses were all very well treated and seemed happy to be out and about with us. The guys that ran the place were equally happy to have us out and they chose the right horses for me and my friend and our very limited riding skills.
We almost decided not to go because when we woke up the weather had taken a turn for the worse. It was hard to get out of bed because the cold was so biting but looking back on it now, I am so glad we managed to crawl out of the covers.
We got a nice little surprise once we were out there too as just as we reached Lake Louise, a light snowfall began to come down on us. Nothing like riding a horse in the Rockies while snow is falling to make you feel like you are a moviestar!
The down side of the snow was that the vision wasn´t great but that didn´t bother me or anybody else it seemed. We had some hot chocolate at the Tea House to warm us up before we eagerly returned to our mounts for the return home. A really awesome activity on a really great day and with a company I would recommend. http://www.brewsteradventures.com/
Best of luck!