Paul Ward, 21, allegedly killed 53-year-old Jean Campbell at Cranhill Park in Glasgow's east end before last Christmas.
Mr Ward also faces a drugs charge.
He appeared from custody yesterday at Glasgow Sheriff Court where he made no plea or declaration.
Thomas Leyden, 22, has been charged with attempting to pervert the course of justice.
He also made no plea or declaration when he appeared in private at the court.
Sheriff Kenneth Mitchell remanded him in custody until next week.
He is expected to appear for a full committal hearing next week.
Consideration of the application for bail for Leyden was continued until today.
Mrs Campbell was walking her German Shepherd-type dog, Kai, when she died on December 13 last year.
Her body was found the following day.
During the high-profile police investigation, detectives made two appeals on the BBC's Crimewatch programme, one in January and another in April.
DNA tests were also carried out locally and a reward of £500 was put up by Crimestoppers.
Officers also turned to social media, appealing directly to Facebook users to help find the killer.
Mrs Campbell leaves behind a daughter Lianne, 34, son John Jr, 33, and husband John.
Lianne made an emotional appeal for help in the second Crimewatch show.
In a statement issued by police at the time, they said Mrs Campbell's family had been left "devastated by the loss of their wife, mother and grandmother and they deserve answers".