As a veterinary student, you won't really be specializing in anything and although you might help a bit with teaching duties you certainly won't be teaching classes to other students.
The AVMA frowns on using terms like 'specializing' unless you've had formal post-graduate training and achieved board certfication in an area, for example
http://www.aczm.org/.
However, certain veterinary schools do provide more exposure than others to exotic and zoo animal medicine. Also, some schools have tracking, where your curriculum is focused in a certain area.