It said some 750,000 children witness domestic violence each year, which can have a "profound and lasting impact".
The charity has launched a video campaign on Facebook, encouraging viewers to raise funds and awareness by sharing the hashtag #givethemrefuge.
The launch comes as Refuge's specialist services face possible funding cuts.
One in four women in the UK experience domestic violence, and two women are killed each week by a partner or ex-partner in England and Wales, the charity said.
Refuge's video shows a girl unwrapping presents while being filmed by her sister, but the children end up abandoning their presents to run away from a violent argument between their parents.
An unnamed 22-year-old abuse victim said the fictional video was similar to her own childhood memories of living in "daily fear and terror" after witnessing her father "abuse, threaten and intimidate" her mother.
"It was only after a frantic phone call I had with my father that I knew he would fulfil his threat to 'smash her brains against the wall' and kill my mother," she said.
She eventually escaped to a refuge with her mother and brother, where they were supported by Refuge, she said.
"Not only did the refuge give us safety, anonymity and a place to overcome our trauma and rebuild our lives, but my brother and I had the opportunity to enjoy our childhood and also start over," she said.
Sandra Horley, chief executive of Refuge, said more than 3,300 women and children were supported by the charity, with children making up about two-thirds of people in the charity's accommodation.
She added that the charity was "fighting to raise funds to keep its services running".
Children, described as the "forgotten victims of domestic violence", have been put at the centre of a Christmas campaign by the charity Refuge.