The oldest known written form of the f-word, AFAIK, is from court records dating to 1310. It involves the summoning to court of one
Roger F--kbythenavele. He was wanted because of his offensive name. You can imagine sheriffs and constables going from village to village asking if anybody knew or had seen Roger F--kbythenavele. At any rate, the f-word is old, and if we have a written source from 1310 then it was probably in use in the 1200s. I've not read or watched Game of Thrones but I suspect the swearing is more frequent than realistic, in the same way that medieval women did not too commonly bare their chests for all to see, particularly considering that they'd only just barely heard of a bath, let alone body waxing.
As was mentioned, a now virtually lost form of English swearing survives only in the minced-oath form, and the words are considered humorous.
Zounds, gadzooks, struth, and so on are the mild forms of "God's wounds", "God's hooks [hands or nails]", "God's truth" and so on. The minced oaths appear in Shakespeare; I'm not sure if they existed in Middle English. Simply using the Lord's name in vain must have been almost as frequent as it is today, even if it were blasphemy when uttered in the wrong place.
Overall, if this is for fiction, strict accuracy is not only virtually impossible but also not desirable. If your characters speak plain English with an emphasis on short Anglo-Saxon words, they should sound natural. Let them say "bloody" or "damned" and try to see if it seems natural for them to swear. You've got an opportunity to develop characters as well, because some may be known as foul-mouthed, and some might never use strong language at all. (Be careful with idioms and expressions, unless they seem old as time. Many expressions are too modern for work set in the 1200s.)
I'd likely be willing to review an example if you wish.