Paramedics were unable to save the 28-year-old from London after she was attacked at Gravelly Hill, Caterham on Thursday afternoon.
Surrey Police detained a total of eight dogs at the scene and detectives are keeping their owners up to date with the investigation. No arrests have been made.
Sue Dove, an eyewitness to the attack recalled the horrifying moment when she saw the woman being attacked by “multiple dogs”.
She told Sky News: “She screamed at us to turn back and with that, two of the loose dogs ran towards us and the horses, my horse spun round and bolted and I eventually fell.”
She added: "(I feel) sadness that a woman has lost her life, but frustrated people are able to walk so many dogs.
"This lady was clearly out of control for whatever reason, had fallen to the ground, being attacked.
"Because of those consequences and two of the dogs running towards us, my horse bolted and I fell from my horse, landing on my right side, on my ribs and hip.
“Fortunately, my horse eventually stopped and my friend was able to get to him. Otherwise, as flight animals, this could have been another horrific accident if he kept going.”
Richard Bream, who runs a nearby kennel said he’d never heard of a dog attack in the area before.
Adding: “That particular area, View Point, is an area where professional dog walkers will turn up in their van and take the dogs out and walk them.
"I’ve always felt you see some of these dog walkers have five or six, and they shouldn’t be able to do that."
Surrey Police said none of the seized dogs had been put down.
Inspector Lyndsey Whatley, borough commander for Tandridge, said on Friday: “This is a tragic incident where a young woman has sadly lost her life and our thoughts are with her family and friends.
“I know that yesterday’s events will be of real concern to the local community and I would like to reassure residents that we are confident all the dogs involved are in the custody of police whilst we investigate the circumstances of what has happened.
“Officers will remain in the area of Gravelly Hill today whilst enquiries continue and if you have any information but have not yet spoken to police then please contact us.”