I think it is due to the cooling, not directly the presence of freezing temperatures, it seems to depend on the plant. It would be a good experiment to see what events contribute to the changes. Clearly the amount of water in the plant contributes to the quality of the color. Stored water is primarily used in the winter months. The loss of leaves and consequently the leave's color change is due to plant's ethylene gas and auxin balance changes.
Ethylene causes aging in plants and auxin levels stimulate growth.
Their levels apparently determine the where the plant grows, where the plant just maintains itself and helps explain dying of selective parts of the plant. This varies widely between species. This change of auxin and ethylene balance apparent triggers the reabsorption of nutrients from the leaf that will be used in the spring to grow new leaves. This process also stops the production of the dark green chlorophyll to replace the chlorophyll that deteriorates naturally in sunlight. Many people do not know that the many plants actually produce some of the colors that show after the green chlorophyll deteriorates at the end of the growing season.