"If we don't take action now," the trust says, "multi-drug resistance could happen in the UK within the next 10 or 20 years.
"This would have a devastating effect on horses and their owners, with horses infected with multi-drug resistant worms potentially suffering the horrific effects of severe infestation."
The trust points out that multi-drug resistance has already occurred in sheep roundworms throughout the world.
Small redworms, or cyathostomins, are a major parasite that can affect horses of all ages.
Horses with a severe infection of these worms can suffer weight loss, colic, diarrhoea and death.
Many horse owners control small redworms, as well as other parasites, by giving their horse regular doses of worming drugs. However, overuse of these is leading to the development of drug-resistant worms.
Only three main types of drugs are available to treat small redworms in horses. Researchers have found evidence of small redworm resistance to each of these drug types individually, and evidence has already been found of multi-drug resistant small redworms in Brazil.
"If multi-drug resistance happens with small redworms, there is no way to turn back the clock - once the worms develop resistance, they will remain resistant and the only solution will be to develop new drugs."
The Horse Trust said it has been funding research into small redworms for more than 10 years.
"Research has led to a better understanding of the biology of the different species of small redworms and how changes in the worms can lead to resistance. Current research is expected to lead to a new test for small redworm resistance, to enable vets to address the issue before it gets out of hand."
The trust said it was also backing an education campaign to stop people from over-worming their horses.
It urged horse owners to support its redworm campaign.