Nose Polyps, Injury, Strenuous Exercise or even Poisoning 
It can be quite frightening for any horse owner who has a nose that bleeds from the nostrils during or after a period of hard work, especially if you have never had a bleeder.(EHIP)
The amount of blood loss can vary from horse to horse, from just a trickle to a gushing constant flow of blood that could be life threatening. If blood drips or flows from one or both nostrils, do not ignore it. The cause of a nosebleed in a horse must be investigated immediately.
Some horses have a history of nosebleeds, especially the ex racehorse, if your horse seems otherwise normal after a loosing just a spoonful of blood, then there is normally no cause for alarm, but call the vet if the bleeding does not stop in a couple of hours. 

Nose Polyps
These are tumors that grow inside of one or both nasal chamber and can only be removed by surgery. Other than a bloody nostril  other indicators may include the horse making more and more noise when breathing, even when standing still, there may also be a foul smell coming from the nostril and mouth. even when standing still and a rotting smell to come from the nostril or mouth.
A bump to the nose or inhaled a foreign object can also cause bleeding from one or both nostrils. If the injury is severe, blood will be flowing from both nostrils and the horse will be showing other signs of distress. A minor injury can cause a sudden rush of blood which can last up to fifteen minutes before it begins to slow. The bleeding needs to be monitored to be sure it stops. If you are unsure you must call a vet.
Extreme and strenuous exercise such as a racehorse being worked out or an endurance horse performing a three- day event may experience bleeding. Due to the level of exercise blood releases itself from the horse's lungs and has now where to escape other than through the nostrils which will continually drip and often form a small puddle of blood on the floor. If the flow continues for more that 30 minutes and gets faster call your vet. 
This is perhaps the most dangerous cause of nosebleed in a horse. Any type of poisoning, your horse will tend to show more signs of distress than just a dripping nosebleed. Depending on the type of poison and the amount consumed, other symptoms may  include bleeding from other bodily openings, bloody urine, sudden lethargy, uncontrollable trembling, suddenly breaking out into a heavy sweat, arching the neck in a bizarre angle, problems walking and seizures.
Living and Management 
Depending on the cause, different steps must be taken after treatment to ensure your horse is healthy and the bleeding stops. A horse with EIPH can usually be managed with certain medications and continue a successful athletic career. However, a horse with a fungal infection will require strong anti-fungal medications or even surgery to remove the infection.
You must never obstruct the nostrils as this may cause a horse to panic - don't forget that horses cannot breathe through their mouths!
If you are unsure then in the first instance always call your vet.

Understanding and taking better care with lots of  A-Z of horse ailments read more