Always best to test your hay. Then you know what you have and if you need to supplement. 10% protein hay in the north is fine for a range cow, as long as they get plenty of it. Sometimes the ranker hay is harder to digest, so if they have more, they can go through it and get the best (you can't fool an old cow) and then work on the remainder in the afternoon. That's what we did and it worked well. Lots of 10% protein hay and we didn't supplement it except with mineral.
There are two ways to be fooled. One is to believe what isn't true; the other is to refuse to believe what is true.