Many plants can withstand temperatures below freezing, many can tolerate temperatures near freezing, but some cannot tolerate low temperatures even when the temperature is above freezing. The time the plant must endure the cold temperature is also a consideration. Longer durations at a low temperature will result in more injury.
Many houseplants are from the tropics and very sensitive to low temperatures.
When I went to my parents' home during the Christmas holidays, I set the thermostat at 50 degrees in my apartment. Later, after several dead plants, I realized that the low temperature killed my flame violet. By keeping the temperature near 60 degrees, subsequent flame violet plants survived without injury. I must also ask how you are measuring the temperature. Temperatures measured in one location may vary by several degrees from temperatures in a nearby location.