As an ex military pilot and horse rider, I too would like to express my condolences. It is possible that a low flying aircraft is to blame. There should be an element of habituation for the horse here, if it was permanently stabled in Lincs, then it should have been well used to the noise and surprise of low flying a/c. So IMHO it is far more likely to be the fault of a lorry driver, a car driver, a motorbike driver, even a cyclist in garish dayglo colours who went past the horse at speed without consideration.
Getting off the horse is not always an option, as already said you have more control on horseback you and out of the way of metal-shod feet. Also, you may not be able to get back on board without a mounting block depending on your and your mount's relative sizes.
If you see a horse/rider on the roads, please slow down and pass SLOWLY and carefully. Remember 500kgs of horse with metal-shod feet is NOT an aircraft, and is not guaranteed to respond to the controls and WILL make a big dent in your prized car. I don't think riders want to jump on bandwagons about low flying a/c, they are far more concerned with trying to raise public awareness of other road users.