The main mechanism behind the scar changing its color is the dilation of blood vessels within the scar tissue. The dilated vessels lead to the congestion of blood flow. The red blood cells moving more slowly leave more oxygen due to its diffusion to the tissue and the hemoglobin -- the oxygen holding protein -- changes its color from scarlet (bound to oxygen) to cyan (released/bound to CO2). Since scars are not covered by skin, the blood vessels are clearly visible here and you see this characteristic color.
The triggering mechanism here is cold that increases the energy barrier for many biochemical reactions, first of all those required for smooth muscle contraction.
Cold-induced vessel dilation (that can be seen, for example, on cheeks and extremities) with mild circulatory disturbances ultimately undergoes into so-called cold vessel paralysis when smooth muscles of blood vessel walls completely loose their ability to contract and are maximally dilated. The cyan color of the scar is usually seen at the very last stage, that can occur unexpectedly quickly because scars do not have any warmth insulation layer compared to the regions covered by skin.