Here's an article I found about this. The part specifically about horse death or injury is on the 6th page, though the rest is actually pretty interesting as well.
http://www.uctc.net/access/30/Access%2030%20-%2002%20-%20Horse%20Power.pdf
In addition, horses often fell, on average once every hundred miles of travel. When this took place, the horse (weighing on average 1,300 pounds) would have to be helped to its feet, which was no mean feat. If injured badly, a fallen horse would be shot on the spot or simply abandoned to die, creating an obstruction that clogged streets and brought traffic to a halt. Dead horses were extremely unwieldy, and although special horse removal vehicles were employed, the technology of the era could not easily move such a burden. As a result, street cleaners often waited for the corpses to putrefy so they could more easily be sawed into pieces and carted off. Thus the corpses rotted in the streets, sometimes for days, with less than appealing consequences for traffic circulation, aesthetics, and public health.
Article references:
Clay McShane. Down the Asphalt Path: The Automobile and the American City. (New York: Columbia University Press, 1994).
Lawrence H. Larsen, “Nineteenth-Century Street Sanitation: A Study of Filth and Frustration,” Wisconsin Magazine of History, vol. 52, no. 3, Spring 1969.
Clay McShane and Joel A. Tarr. “The Centrality of the Horse in the Nineteenth Century American City,” in The Making of Urban America, ed. Raymond A. Mohl (Wilmington DE: Scholarly Resources, 1997).
Nigel Morgan, “Infant Mortality, Flies and Horses in Later-Nineteenth-Century Towns: A Case Study of Preston,” Continuity and Change, vol. 17, no. 1, 2002.
Joel A. Tarr, “The Horse: Polluter of the City,” in The Search for the Ultimate Sink: Urban Pollution in Historical Perspective, ed. Joel A. Tarr (Akron, Ohio: University of Akron Press, 1996).
Francis Michael Longstreth Thompson, ed. Horses in European Economic History: A Preliminary Canter (Great Britain: British Agricultural History Society, 1983).
I have a followup question :
Any reason people (the poor?) would not just cut up and eat the horse?
May I ask as a follow up who would shoot an injured horse? Did people have their own firearms? The local police patrol?
Along the same lines I was wondering what would happen to your vehicle if your horse died? Was there a service to get a temporary horse to pull you where you needed to go? Or just buy a new horse?
Another question: I'm living in 1900 and am tired of walking, so I want to get some wheels. How much does a horse and carriage setup cost? Where do I buy it? How often do I need to replace the carriage or horses?