Most of my income is from equine photography and I do insist that they turn on the sun and turn off the rain. Actually, it's the rain as it's not just the camera I don't like getting wet but also faces and people carry their heads lower in the rain - no harm on saying "weather permitting" in my book and most people understand.
Good old fashioned sun from over the shoulder and get down to face level, especially with ponies and children is an easy starting point.
Other than that, the shots that sell are: pricked ears on the horse/pony, smiling children and after that, a decent background without distractions like a car's front wing or a dustbin or a horse rug left on the floor.
You obviously know that people blink - some more than others. Well, horses do as well and nearly as much. So it's frequently worth taking 3-4 images of the same sort of shot. And a horse's blink is slower than a human's and not so visible when looking through the viewfinder.
Legs and jumping - this is getting more advanced but is very important in equine photography. If they're standing still, it's usually best to ensure all four legs are in view, so move around until they are. No need to photograph full length for every shot though. And if you do full length make certain you have all the hooves in and the top of the rider's hat. When moving, you're looking for an M shape in the legs. In a trot, watch the far rear leg and as soon as it touches the ground, click the shutter button. If they're jumping wait for a moment when the pony/horse is leaping as it's about 1/2 second from the upright stance to leaving the ground - in the air is what you're aiming for but also on the rise if the horse is coming towards you - sideways on you want the horse nearly flat in the air.
Most important, go and enjoy yourself - they're asking you because you can do a better job than they can. And if it doesn't work that well, return for another go
