Christine, There are many many different types of bamboo. Some are winter hardy here and some aren't. You are right to worry about their spread. Most of the hardy bamboos spread vigorously by rhizomes. Guess Im not sure if you are leaving the horse tank above ground or burying it. If it's not buried Im not sure if the bamboo will overwinter. And if the drainage is not good Im not sure they will live in it. The American Bamboo Society has some great info you may find helpful.
http://www.americanbamboo.org 
