The body of Fiona Southwell, 59, was discovered at Grange Farm, Goxhill Lane, Seaton on Friday evening.
The 21-year-old man, who is understood not to be a relative, is in custody being questioned by detectives.
Mrs Southwell is believed to have been a freelance artist, who took commissions for horse and pet portraits, and was a member of Hornsea Art Society. She also worked as a freelance riding instructor.
Locals said she had lived at the isolated farm, which is down a single lane track, for around 18 months.
Today specialist officers were searching the verges of a dirt track leading to the Hull to Hornsea cycle path, which was busy with cyclists and walkers.
Cordons have gone up at the farm and at an address in Hornsea as part of the investigation.
Specialist officers have been deployed to support Mrs Southwell’s family.
Detective Chief Inspector Tony Cockerill, who is leading the investigation, said: “Fiona Southwell’s death is being treated as suspicious and a team of detectives from the Major Incident Team and other departments are carrying out a large number of enquiries to establish how she died and identify the those responsible.
“We are supporting the victim’s family and keeping them informed about developments in the case.
“There has been an arrest in connection with the murder, however we still need the public’s help in piecing together the circumstance of Fiona’s death.
“I would specifically like to speak to anyone using the old railway track between Hull and Hornsea between 7am and 7pm on Friday who may have seen something suspicious or untoward.
“The track passes the farm and is well used by cyclists and walkers and would urge people using the track to call us think if they can help.
“Your information no matter how small could hold the key to establishing the circumstances of Fiona Southwell’s death.”
Stephen and Annmarie Sharp, from Kirk Ella, had been walking on the track back from Hornsea. Mrs Sharp added: “We were walking back from Hornsea and saw police with sticks searching. It’s such a shame, how awful it is. This is such a family orientated place and so peaceful.
“But I was just saying I wouldn’t come here on my own, it is too isolated.”
Her husband added: “I am really shocked it is a really nice part of the world.”