They made the appeal a week after Penelope Davis, 47, known as Pennie, was found stabbed to death in a field where she was tending to her horses.
Her five children and husband said they were "overwhelmed" by people's support.
Crimestoppers has offered a Â£5,000 reward for information leading to the conviction of the killer.
A 22-year-old man arrested on suspicion of murder has been released on bail.
Hampshire Constabulary said it was possible Pennie may have been followed on the day of her murder, on 2 September, from the local supermarket where she worked to the horse paddock.
Her children, Sophie, Alex, Georgia, Daniel and Josef, and her husband Pete, said in the statement: "It has been a long, agonising week since our precious mum and wife was selfishly taken from us.
"We had no idea how many lives she had touched, as we have been overwhelmed by love and support. Despite this, the void in our hearts only continues to grow.
"The police have made progress, but there is still much more to be done. We only hope that no other family should ever have to go through the ordeal that we are currently facing.
"No other person deserves to ever have to go the way our poor mum and wife did. We will never begin to understand how scared and how alone she must have felt.
"This is why we are pleading for anybody with any information to come forward. Even if you think it won't make a difference, it might just be the call we were waiting for."
The mother-of-five's body was found by her husband in the paddock near Leygreen Farm in Beaulieu. A post-mortem examination revealed she died from multiple stab wounds.
Mrs Davis, from Blackfield, worked in a local supermarket and visited the field daily to tend to her horses.
Police would like to hear from anyone who may have seen or heard anyone acting suspiciously near Sainsbury's on Hampton Lane, Blackfield, between 13:00 and 15:00 BST on 2 September.
The children of a woman who was murdered in the New Forest have made an emotional appeal for information to help catch their mother's killer.