How much cold can a poinsettia withhold?

No, poinsettias (Euphorbia pulcherrima) cannot tolerate cold.

Specifically, poinsettias are native to semi-tropical and tropical areas of Latin America. They tend to prefer a temperature range of 60-80 degrees F/15.56-26.67 degrees C. Once temperatures drop below 60 degrees F/15.56 degrees C, poinsettias become susceptible to the black rot of Thielaviopsis basicole. When temperatures drop down to 55 degrees F/12.78 degrees C, poinsettias will find their flowering affected. When temperatures drop even further to 50 degrees C/10 degrees C, poinsettias suffer irreversible injury.