I don't think tai chi is working with the scientific idea of energy. I'm sure there are ways to control and use your body language and the impulsion and forces your body can produce to do all kinds of wonderful things, but describing them in pseudoscientific terms is just asking for trouble with people like me xD
Basically, I'm sure that the things people do in systems like tai chi to control their body or, in your examples, communicate with your horse, are valid. But they're not using the word 'energy' in any kind of scientific sense.
How can you transfer energy from one body to another? Depends on the type of energy. You can increase an object's kinetic energy by accelerating it and increasing its velocity: if you pushed a 1 kg block hard enough to change its velocity from 1 m/s to 3 m/s its KE would change from 0.5 J to 4.5 J. If you put a spoon into a bowl of hot water, heat energy will transfer from the water to the spoon, raising its temperature.
I have a module at uni called Transport Phenomena. Half of it is all about heat transfer and how you heat things up and cool them down. The other half is all about mass transfer - how you move kinetic energy (and do other kinds of work) on fluids and stuff. If you want to know about heat capacities or enthalpy or momentum transfer ... well, ask me once I've gone over my notes xD Edit to add:
I think that these people are using the word 'energy' to make people think about how they are moving their bodies and so on and as an aid in getting the right kind of movement or stance or so on. It's a word they use to help the people visualise what they need to do, rather than a word that scientifically describes what's going on.