I also have never come across a historical description in English or Chinese

A "Cold Palace" (冷宫), as portrayed in literature and film, was not necessarily a set location since it was more of a "cold shoulder" situation. Whenever a prince, princess, concubine, or anyone else who had fallen out of favor but were not allowed to leave the imperial palace (not necessarily the Forbidden Palace, although that is the most popular one), that would qualify as being in a "Cold Palace" (打入冷宮)

Of course, the person would usually be confined to a small dank place and kept under watch, unless their offense was relatively light and they still had powerful supporters, in which case the person could merit a somewhat decent location or even stay in their original quarters