Any temperature of 55 F or below 55 F is too cold for sleeping.
However some people get better sleep when the bedroom temperature is 50 F but any lower than 50 F is too cold in my opinion.
You should maintain a house temperature of between 55 F to 60 F at night and if you have kids or babies in the house keep the temperature above 60 F because kids and babies are colder than adults.
It's not bad to sleep in a cold room as long as the cold room is not too cold.
Research has shown that people get the best sleep when the bedroom is 65 F or cooler at night as the cool temperatures help you fall asleep.
However you do not want your room to get too cold as that can cause illness and make you sick and prevent you from getting enough sleep.
I would say any room temperature that is cooler than 55 F would be too cold for sleeping.
But any temperature of 55 F or above is an okay cool temperature to sleep in.
During the winter I turn down my heater thermostat to 60 F which is cool enough to sleep.
That is because I'm also under my blankets and am warm enough.
But in the day the thermostat in the winter is set to 75 F which is how I like it.