Sweating during physical exertion in cold weather is a well-known physiological response driven by metabolic heat production, and no citation is needed for this everyday biological fact.
The claim that sweating occurs during cold-weather walking as a normal physiological response is a matter of everyday observation and basic human physiology (metabolic heat generated by exercise must be dissipated via sweat even when ambient temperatures are low). Therefore, this is classified as common knowledge requiring no citation.