The temperature was only 3C and the girl left the property, later being spotted on the road by a passer-by who phoned police.
The 3-year-old could not tell police her surname but managed to point out the house she lived in, which was empty when police knocked.
The girl's mother was later seen "staggering up the road, intoxicated".
Judge Walsh accepted a plea from the woman's solicitor Frank Minehan that supervision was appropriate.
He said the woman had no previous convictions and he had read a letter from the woman and one from her church pastor.
"What you did put your daughter at risk," Judge Walsh said.
"If she had come to harm you would have had to live with that for the rest of your life."
He said Child, Youth and Family and the girl's grandparents had been involved in caring for her since the incident.