The incident is thought to have happened last week on Horsehold Lane, Hebden Bridge, where Tinkerbell and Twinkle are kept.
Owner Darren Cole, 37, from Cornholme, Todmorden, made the discovery when he made his nightly visit to check on his ponies, which he has kept for around 15 years.
He said: “I went up at night to see them and I found the tails had been cut just below the bone.
“They haven’t been injured, but they will be in discomfort with it as at this time of year, they use the tail to swat away flies.
“It has happened before. I’m really annoyed by it and I just can’t think why somebody would do it. Last time, it was said that people make things out of the hair.”
He added that it would take a year or more for the tails to grow back and they are being fitted with false ones over the weekend.
Pc Jonathan Sutton, of West Yorkshire Police, said: “Any incident involving pets is of course extremely distressing for the owners, and whilst the animals were not physically harmed there will be understandable concern in the community, particularly amongst those who keep animals or livestock outdoors.”
Leanne Plumtree, of the RSPCA animal charity, added: “While it can be normal practice for owners to trim the hair on their horses’ tails, it’s concerning that a stranger appears to have done this.
“Sometimes other horses can chew manes and tails but if it’s a clean cut, it’s good to be vigilant and report any suspicious behaviour.”