Vanzant, who has a 4-year-old son and was going through a divorce, went shopping with her mother at a local dollar store before getting into the car with Brown that day.
"They were just going to drive around," her mother, Tina Penix, said. "It snowed that day and it was pretty."
But while Penix alleged that Brown dropped her daughter off in a dangerous area known as McCausey Ridge, Brown said he dropped her off on the main road that leads to that area.
Tina Penix said her daughter left town once before without telling anyone, but she called within a day and told them when she'd return. She'd never just left for long periods of time without telling anyone, Penix said, and she did not have a cell phone.
"I'm just worried sick," she said.
Tina Penix hopes her daughter simply took off on her own, but said she's worried Brown might be involved with the disappearance.
"We were trying to keep her away from him," she said. "He was a weirdo."
"I would never hurt her," Brown said. "I love Nicole. I care very much about her. But the girl is hooked on pills, bad."
That night in the car, Brown said, he was trying to talk her out of getting more pills and to "grow up." When she got out of the car, Brown said, "she said 'I'll find someone to buy me a pill.'"
The Menifee County Sheriff's Office has called in several agencies, including the Kentucky State Police and a Texas-based team that searches on horseback, to help with the investigation, though a snowstorm this week has halted the ground search until the weather clears.
The rural county includes Daniel Boone National Forest and is full of trails and cliffs and difficult terrain.
Menifee County Sheriff Rodney Coffey told ABCNews.com that his office's dispatch center had been getting anonymous tips about where she might be, including hiking trails and a county park. They've looked at some hard-to-reach places using the Fire Department's search and rescue team.
"We have so many hiking trails and so many hangouts," he said. "So far we've not turned anything up."
For now, Vanzant's son is staying with his father about an hour and a half away.
"I can't talk to him because I'm scared he's going to ask where Mommy is," Tina Penix said. "I don't want to lie to him."