Grizzly Bear vs Horse

"Swift too, is he, in amazing measure for his build. Those who form their idea of a bear's speed from watching a hulking, slouching prisoner, are sure to be amazed at the real thing. For 50 or 100 yards a Grizzly can go faster than any horse, and keep it up indefinitely. It is well known that in the spring of the year, the Indian ponies that have wintered out and are poor, very commonly become the prey of the Grizzly, who can now catch them on the open plain. Townsend tells of a wounded Grizzly that pursued closely a man on horseback for half a mile, snapping at the horse's heels, and apparently would have captured the object of his wrath but for a timely volley from the man's comrades.

Source: https://www.nps.gov/parkhistory/online_books/yell/vol14-1-2a.htm