Ayana McClinton, 31, faces two counts of child endangerment, according to court documents.
The Harris County Sheriff's Office said deputies responded to a 911 call at around 6:40 a.m. on 12062 Veterans Memorial Drive after someone reported seeing the woman and her babies lying on a sidewalk.
HCSO said the 30-year-old mother showed signs of intoxication, and she decided to take a nap outside on the ground with the outside temperature around 28 degrees.
Authorities said the woman had an open alcoholic beverage near her.
First responders arrived and treated the 2-month-old and 1-year-old babies, who suffered cold-related injuries.