I've tried web search but have not found that specific answer. As far as I know at least some people feel pain (e.g. in fingers) when exposed to cold for prolonged amounts of time. E.g. here sciencedirect - thermoreceptor
The temperatures that individuals report as painful vary, although temperatures above 45 °C and below 15 °C are generally considered to be painful.
As I understand 15 °C refers to ambient temperature, probably when full body is exposed to it for prolonged time resulting in gradually drop of internal temperature. But at what temperature at the thermoreceptors (nerve sensory endings) pain signals are produced and after what time threshold? Are they (temperature level and time duration thresholds) same for different parts of the body?
That answer here Why do people feel extreme cold at different temperatures compared to other people of same body structure? implies feeling depend on many things, like differences in clothing, distributions of body fat which does not look like they would change an answer to my question and some others, like neurotransmitter sensitivity which look to me like they could. However, I think there could be definitive answer to my question in the form of a reasonable range.