References are good. Insurance is vital. If they don't have haulers insurance (here you can also get it thourgh EC) and they get into an accident, your horse won't be covered and that's your loss.
I pay someone to haul my horses all the time (she is picking up my colt from California and bringing him to Alberta in six days) and he is completely insured in her trailer. He also has extra insurance through my broker here as well.
I took a $10,000 loss and learned the hard way. REALLY check into their insurance.