No, bristlenose plecos cannot live in cold water. As tropical fish, they require a warm temperature between 74°F and 80°F (23°C and 26.5°C) to thrive.
If the water is too cold, especially once it gets below 60°F (15.5° C), the fish will suffer from various illnesses, fatigue, stress, and growth stunts. If left in cold water for too long, these fish will eventually die.
For that reason, you should keep their tank warm by installing a heater. Adjustable heaters with built-in thermometers are preferable, so you can easily maintain the optimal water temperature.