We are next to a livery yard, the entrance runs right past the end wall of our house (we bought the farmhouse, but not the yard next door).
Mornings from 6ish, never heard before, we may get the clip clopping of hooves beside the wall as people are turning out. Again in the evening, but yard closes at 9pm. The farmer does come and go on his tractor, very late in the summer months, but it isn't a problem.
The muck heap is well away from the house, although there is a horsey smell sometimes from the yard. There is also a sand school just over the fence and the only time we have heard annoying noise, was someone who was having lessons from a very noisy and shouty instructor at 8am on one Sunday morning! Luckily it only happened once or twice.
Generally, there is not much problem, we live down a dead end lane and of course we get cars coming and going to the yard, but the owner has strict rules over who can come into the yard and won't open earlier than 6 and closes the gates at 9, unless they ask speciically.
A riding school may be different, more kids running around and shouting, more cars coming and going, risk of security of strangers being around.
The best bit is that 11 years on from buying the house, our now 7 year old has started riding and we have a pony literally next door - something I only dreamed of as a horsey kid, I can't tell you how great it is to put the kettle on and go and feed the pony and get back in time for it boiling.
If you are not horsey, then think carefully, but if you are happy with country smells and sounds, it will be fine.