Hi Mike,
I live up here in Ayr and used to cover the racing for the local newspaper. Ayr Gold Cup, Scottish National, plus all the local meets. Is it jumps or flat?
If Jumps:
Get to the inside of the track and go for low angles up against the final fence works well. Take into consideration to the position of the sun and make sure you are not standing in potentially dangerous place.
If Flats:
Position your self on the outside at the last corner but back a bit. Use the longest lens you have and try manually focusing on a point on the ground and the releasing the shutter as the horses cross the point. "Trap Focusing"
Remember to go for variety so don't just concentrate on the actual races. Go for reaction shots from punters. Photograph the "Tic Tac" men and women doing there thing and cover the whole day.
Other Ideas:
Try a slower shutter speed and pan with the horses as they pass you for effect.
Pre-focus on the winners post and then use a slow shutter speed around a 1/60th to make an image of the horses passing blurred etc...
Race days are great for silhouettes, (Weather dependant) So try positioning the sun directly behind horse and jockey and meter for the sky.
Try find a high vantage point and shoot an overall wide shot of the day when the crowd is at its peak and there is a race finishing over the line.
Look for close-up details shots. Riding Crops, Riding Tack, Muddy Boots, Book Makers Badges, Coats and Hats, There is loads going on...
Horse racing is a great leveller for a photographer because you have a mixture of Sport, Portraiture, Animal, Street and landscape photography all in one place. So enjoy yourself.
Finally don't use flash or make an excessive noise around the horses. They are skittish at the best of times...
I hope this helps and drop me a line through the website and let me know how you got on.