There's a sign like that in my area.
It's a narrow road going about half way up a local hill to a small gathering of 5 or 6 houses, where it dead-ends shortly after. The locals, fed up with people driving up the hill, parking their cars, and leaving them as they go off for a walk, put up numerous "No Entry" and "Private Road" signs.
On all the maps it's a public right of way. Check the maps for your area, and it might be the same.
Edit.. Cross posted with you - Good to hear that it is in fact a bridle way.