We call that ett hårstrå in modern Swedish. You can find ett hår for a single strand of hair in old texts, but I don't think anyone says that today. I certainly wouldn't.
That's not unreasonable; I was basing my assumption off of the fact that ett snöre means a piece of string as well as a string – probably not the most logical comparison to make! Tack!
Wouldn't it be a more accurate translation to say "My hair has turned grey"
Because in English speaking countries you get grey hair (not white hair) when you get old :-) Interesting enough, we say "graue Haare" (grey hair) in German, but it is "rambut putih" (white hair) in Indonesian.