However, they believe that more than one person could be involved in the assaults, which this month spread to Buckinghamshire and culminated in the death of a mare last weekend. Police also issued a description of a second man.
Since January 1991, 23 animals have been attacked, mostly in the Meon Valley, Hampshire. One cow was also attacked last year.
Many of the attacks have had a sexual nature, with mares' genitals being slashed. Police said two horses and a cow had to be destroyed in Hampshire last year. In Buckinghamshire, there have been three incidents this month.
Last weekend, a 12-year-old mare, Mountbatten, was found dead in her stable near Alton, Hampshire. She was the first horse to be killed.
Police said they had received more than 600 calls since launching 'Operation Mountbatten' to find those injuring the horses.
Detective Superintendent Peter Long, of Hampshire Police, said: 'I am clear in my own mind that these attacks are not confined to one individual. There may be a series of people committing these offences.'
The man in the photofit is about 5ft 7in tall with mousy hair. He was seen in the Alton area where the cow was attacked on 3 or 4 October last year. The second description is of a man aged 60 or 70, about 5ft 3in tall, with a ruddy complexion and grey hair, who was seen interfering with a mare at Alton in March 1991.
Rewards of up to pounds 18,000 have been offered by horse lovers and horse associations for information leading to the attacker.