Ligament injuries should not naturally be sensitive to cold; however, due to impaired blood circulation in the damaged area or poor blood supply due to scar repair, the circulation in the injured tendons becomes worse compared to other areas. In cold conditions, this can lead to even poorer blood flow. When circulation is poor, it's hard for metabolic byproducts to be removed from the area, leading to their accumulation, which can stimulate the injured site and cause pain. Therefore, areas with ligament injuries often become sensitive to cold, as the cold causes blood vessels to constrict, leading to the accumulation of metabolic by-products and resulting in pain at the affected site.