Jean Campbell's husband went to look for her after she didn't come home and found her body.
The 53-year-old's body was found in Cranhill Park - just yards from her home - on Saturday morning.
Police have stepped up their hunt for clues and are trying to find a motive for the killing.
Around a dozen officers remained at the scene yesterday, guarding the park, and forensic experts were carrying out investigations.
Horrified neighbours told of their shock after the mother-of-two was murdered.
And it emerged calls have been made for improved lighting and increased CCTV in the park. An online petition calling for these changes has already received more than 420 signatures of support.
One woman, who did not wish to be named, said: "It makes you think twice about going out a night. The park needs to have better lighting, you don't know who is about. It's very frightening."
A Glasgow City Council spokesman said: "This is a shocking and tragic incident, however it is important that people remember that crime levels in our parks are relatively low.
"The council will continue to work with Police Scotland, Community Safety Glasgow and other partner agencies, to tackle all forms of crime."
Detectives have been speaking to her neighbours in an attempt to piece together Mrs Campbell's final movements.
Police patrols are being stepped up in the area after her body was found at around 7.40am on Saturday.
Extra high-visibility patrols have been deployed around the park in a bid to reassure concerned local residents.
Forensic experts in white suits were seen working in Cranhill Park and a protective white tent had been erected.
Mrs Campbell was last seen by a family member at about 5pm on Friday.
She left her flat in Bellrock Street to walk her German Shepherd. Her dog was later found in the park off Bellrock Street.
Police Scotland said a post-mortem has taken place and police are now treating her death as murder.
Officers are carrying out door to door inquiries in the local area and checking CCTV footage.
Detective Chief Inspector Colin Carey, who is leading the investigation, said "extensive inquiries" are under way.
He added: "I would urge anyone who saw her between 5pm on Friday and Saturday morning to come forward.
"Her German Shepherd-type dog was with her in the park, so we are trying to establish when she left her house to take the dog for a walk."
Anyone with information is asked to contact police on 101.