I haven't personally tried them but in my mind there is no doubt that some oils relax muscles or calm horses etc. Lots of conventional drugs are actually plant extracts so using the plant oils have small concentrations of those medicines in them.
Im trying to think of an oil exapmles off the top of my head but failing...
Ooh chamomile flowers (i think they can be made into oils...
) have a chemical called chamazul-something which is actually an antiallergic drug but chamomile also calms and sedates.
Another is willow trees. Its not an oil, but painkillers are derived from it so munching on willow branches will provide some pain relief.
However, be wary of 'mirical' oils. Many plant extracts have been used for centuries and have been proven for their medical properties, but companies exploit this and come up with 'newly discovered properties' or entirly new extracts which are as useful as giving water to a horse to try and calm it down haha
Experiment with your horse though, can't hurt!