As long as the baby is healthy overall then the baby is unlikely to die from a cold.
But if the babies immune system is compromised at birth or they were born premature then the risks of death go up when the baby has a cold.
If you think the babies cold is getting worse or it's not clearing up either see the babies doctor or go to urgent care or the emergency room just to be safe.
If the baby is congested a lot and cannot breathe properly then I would recommend taking them to the emergency room or urgent care for treatment.
It's better to be safe than sorry later on.
However most cases of cold viruses with a baby are not very severe and usually resolve on it's own within a week to 14 days.
If the babies congested and cold lasts longer than a week or 10 days then you should take the baby to the emergency room or urgent care center or at least take the baby to the doctor.
Use a humidifier in the babies room and make sure they are staying hydrated and having enough wet diapers during the day.