I'm sure if you go on the forestry website it tells you where it's horse friendly! I'm fairly local but still haven't got round to it after 15yrs of having my own pony/horse...... or holkham....!!
Holkham is one I want to try too!! I've only been here a year, there seems to be loads of places to ride, don't really want to try them on my own though!
I know what you mean about not wanting to go about on your own, I try and do quite a few of the sponsored rides, done a lovely one at west acre earlier this year but got soaked!!
Take a map, I went once and got completely lost, thankfully two other riders were out and rescued me Holkham is great £7 to park lorry/trailer then a beautiful safe beach to play on