Chinese Medicine says that you shouldn’t ride your bicycle with your back exposed, but so did my cycling coach in the 80’s.
Both accept the common sense wisdom that exposing your back to cold and the draft of moving air is a bad idea, and that it can lead to lower back stiffness and pain. Chinese medicine goes further and holds that such exposure can affect the Kidney organ /meridian system and lead to general weakness, poor endurance, and fatigue, or even urinary or reproductive problems.
Old school cycling jackets were made long to cover the lower back. If they don’t match your style try to wear a top that reaches your bottoms, or tuck your singlet or shirt in. Try channelling Eddy Merckx.