Horses are a fun, comfortable way to travel. Saddle horses, pack mules and draft horses are able to reach areas that even four wheelers and dirt bikes have trouble. A policeman on horse back is both an visible symbol of authority and an easily approachable one (horses have fuzzy faces kids love to pet). Policemen on horse back, shoulder to shoulder with shields and batons are about as effective a tool against rioters as is available. The physical effect of a mounted, armed man on a man on foot has not diminished with time.

However, I don't think that horses can be a viable replacement for the widespread use of gasoline or electric powered vehicles, either in urban areas. The month of September was the first time in more that 15 years that new car sales in the United States dropped below 1 million(according the the Korea Herald).
-Grain stores for a million horses would a major health hazard in terms of attracting rodents and insects.
-1 million horses produce a vast amount of manure.
-Horses require up keep and training most Americans don't have and have no interest to invest in. The Walmart and Gap crowd simply aren't going to get involved in horse transport.
-Over long distances horses don't compare in speed to any form of public conveyance. Over short, urban distances a whole new infrastructure would have to be built to accommodate horses and would concentrate the problems that horses present.

Without a major energy crunch and a massive drop in population, I don't see horses ever replacing more modern locomotion for most purposes.