The Highway Code is a valuable resource which you should check often.

Rules about animals.

Always take extra care when you are in the vicinity of animals.

Some drivers display a lack of care near animals that shows a distinct lack of respect for the animals, who when all is said and done; have usually no choice in being there.

Horseriders

34: Safety equipment. Children under the age of 14 MUST wear a helmet which complies with the Regulations. It MUST be fastened securely. Other riders should also follow this advice.
Law H(PHYR)R

35: Other clothing. You should wear

36: At night. It is safer not to ride on the road at night or in poor visibility, but if you do, make sure your horse has reflective bands above the fetlock joints. Carry a light which shows white to the front and red to the rear.

Riding

37: Before you take a horse on to a road, you should

Always ride with other, less nervous horses if you think that your horse will be nervous of traffic. Never ride a horse without a saddle or bridle.

38: Before riding off or turning, look behind you to make sure it is safe, then give a clear arm signal.

39: When riding on the road you should

40: You MUST NOT take a horse on to a footpath, pavement or cycle track. Use a bridleway where possible.
Laws HA 1835 sect 72 & R(S)A sect 129(5)

41: Avoid roundabouts wherever possible. If you use them you should

Other animals

42: Dogs. Do not let a dog out on the road on its own. Keep it on a short lead when walking on the pavement, road or path shared with cyclists.

43: When in a vehicle make sure dogs or other animals are suitably restrained so they cannot distract you while you are driving or injure you if you stop quickly.

44: Animals being herded. These should be kept under control at all times. You should, if possible, send another person along the road in front to warn other road users, especially at a bend or the brow of a hill. It is safer not to move animals after dark, but if you do, then wear reflective clothing and ensure that lights are carried (white at the front and red at the rear of the herd).