The 27-year-old woman was arrested after two people spotted the children, ages 23 months and 10 years, in the car, the police department said in a news release. The vehicle was locked but not running.
Officers responding to the scene Wednesday evening were approached by the children's parents. The father met the mother at the tanning salon and was arguing with her about why the children were in the car, police said.
The children were dressed warmly, but they had "goose bumps" from the cold, the release said. They did not require medical attention.
The temperature at the time was 12 degrees, with a wind chill index of about minus 2 degrees.
The woman could be charged Friday with two counts of misdemeanor child neglect, police said.
"She said she was going on vacation and felt that the tanning was a priority," Lt. Jeff Johnston said Friday.