Years ago there was a stable on Ambergris Caye, but it's no more.
There is horseback riding at a number of the mainland lodges. Banana Bank near Belmopan has the most horses (the owner, John Carr, is a former cowboy and rodeo rider), and M.E.T. near San Ignacio is well known for its horses, too. But quite a few other lodges, including Chaa Creek and duPlooy's, do horseback rides.
Belize books and publications by Lan Sluder:
Belize First Magazine (http://www.belizefirst.com
Fodor's Belize & Guatemala Guide (new 4th edition coming this summer)
Adapter Kit: Belize (the first and only comprehensive guide to living, retiring, working and investing in Belize -- a best-seller on Amazon.com)
San Pedro Cool (the first and only visitor guide to Ambergris Caye)
Belize First Guide to Mainland Belize
UpClose Central America
Belize Book of Lists