What would you call someone who specializes in big cats, bears and wolves? I'm interested in becoming a vetenarian and would like to know the area or areas that I should focus on if I want to work with big cats, bears and wolves.

You'll have to do some research around this but from my basic reading I think you need to do large animal specialist training:
https://en.wikipedia.org/wiki/Veterinar … ed_Kingdom

and to add - the number of jobs available working with thoise animals will be limited even in Zoos.