If you already own a suitable Truck and Trailer, there is money to be made, not sure if it would be a lot or a little.
To go out and purchase a Truck and a Trailer for the purpose of Transporting Animals would be a very risky venture, IMO
Having friends in the Transportation Industry in general in today's economy, the key is to have Lots of Contacts in the type of Transportation business you are interested in.
Proper Insurance, Equipment and References are a Huge Prerequisite, yes I know it is hard to get references when starting a business, thus the Contacts, Friends and others that can vouch for you till you get a few Clients under your belt will help greatly.
Maybe contacts some Vets, Farriers and Neighbors to help spread the word and get a few Clients, then your Job of acquiring new people who do not know you to haul for will be easier because you will have references.
Good Luck with your venture