Horses- where’s the balance?

I was driving on some back roads earlier that I know very well, and as I came up to a part that becomes NSL I quickly got myself up to 60. As I do, I go past a few oncoming cars, then a lady on a horse behind them.

Now, I couldn’t see the horse until I passed the last car, and I assumed they had all gone slow for the 30mph I’d just left. Therefore it was too late to slow down to the usual horse passing speed, and the woman starts flapping her arm.

I stopped, honestly expecting an argument, undid my window, and said ‘is there a problem, are you okay?’ She then said she was concerened about my speed so was getting me to slow down. She then mentioned that a law had come in saying you have to slow to 10mph to pass horses. I said fair enough, I’ll admit I didn’t know that, apologised, then drove off.

She was happy, I felt somewhat embarrassed but at least I apologised and learned something.

Now my question is this- are horse riders fair to expect full consideration on roads? I have no problem with it in general, but today this horse rider not only chose to go on a road that is NSL, but I also genuinely could not see her and had to brake very harshly for her.

Would I be fair to suggest that maybe horse riders shouldn’t be using NSL roads if they don’t want to get spooked, or have I just messed up?