Cold and pale often go together with wounds caused by poor arterial blood flow.
Symptoms of these wounds, called ischemic ulcers, include a leg that turns pale and cool to touch when you raise it. Dangling the leg down off the side of a bed or chair causes the leg to turn red.
The skin on the leg can appear shiny, tight, dry and hairless. The wounds themselves may appear on the legs, ankles, toes and between the toes.
The cause behind all of it is the same. Narrowed arteries prevent a healthy supply of blood from flowing to the legs, so the tissues don’t get enough nutrients and oxygen.
There is a separate instruction about color if you have diabetes: contact your provider if your foot ulcer is very white, blue, or black. This stands on its own, apart from the signs of infection, and you don’t need to work out what the color means.
Wounds that are pale, purple, or black are less likely to heal.
There are also two practical steps, and the reason is in this question: protect your feet from the cold, and do not soak your feet in hot water. For anyone with reduced feeling in their feet, the second one prevents burns, because the skin does not respond normally to heat.
Nothing here can tell you what is happening in your foot. Cold, pale toes alongside a wound are a reason to have the circulation checked, which is part of what happens at a wound appointment.