The charity was called about the horses on land off Gelderd Road, Morley on Sunday, January 20. One of the horses had to be put to sleep on the advice of a vet.
The colts - the term given to young male un-neutered horses - are described as small cob-types.
RSPCA inspector Dave Holgate said: “One of the horses was collapsed when I arrived.
“A vet and police came to the scene with me - and a couple of other inspectors were there to help me handle the other horse.
“I managed to get the down horse back up on his feet and the vet believed he might have a chance so he was transported to their practice for further care and checks, but very sadly his condition worsened and he was put to sleep on their advice not long after arriving.
“He was underweight and suffering from a suspected heavy worm burden.”
The surviving horse was treated for worms and is now in RSPCA care at a private boarding establishment.
Inspector Holgate added: “Thankfully the second horse is in normal body condition and will go up for adoption if no one comes forward for him.
“It’s heartbreaking to have to deal with horses like this. These are just youngsters, last years’ foals who have been dumped because no one wants them enough to provide for them and give them the care they need.
“If anyone has any information about who is responsible, please call the inspector appeal line on 0300 123 8018 and ask to leave a message for me.”
The colts are just two of the many horses dumped as the RSPCA and other animal charities struggle to cope with an ongoing equine crisis.
The RSPCA’s inspectorate national equine co-ordinator Christine McNeil said: “Up and down England and Wales, horses are being found sick, dying or sometimes dead. It is frequently the case that they have been abandoned and left to die. This is upsettingly very common and it’s a massive issue - a very sad one at that.
“We are constantly receiving calls to our cruelty line - on average 80 per day about horses alone across England and Wales - as well as messages every day on social media from very concerned and upset people asking for our help.”
Find out more about rehoming rescue horses, visit www.rspca.org.uk/findapet/rehomeahorse