I've never seen or read any of the ASOIAF/GOT series, but just going from that Wiki article, I would say that if there's a martial sect at the Great Wall, I think the Chinese imperial court would be much more concerned and attentive to affairs, and much less likely to ignore them.
So, perhaps . . .
The best time frame would probably be the Ming Dynasty, against the Mongols and the Manchus. Let's say this order is based at the Wanli Temples, or 萬里寺, so you'll probably want to have one at the main passes (Shanhai, Jiayu, etc). Each temple will be constructed like a fortress, attached to the Wall directly. Each will have a Chief Abbot, but the overall head of the order will be somebody else, based from the greatest temple. Due to the Chinese tendency for centralization, I could actually see the headquarters being based out of Beijing. It would still be a hard life in one of these military monasteries, so the people that would join would be perhaps the outcasts of society, who flee for military service in order to escape debts or something, and in the process, get inducted into a highly disciplined order.
I guess that's a start.