In reply to petegunn: Locate which parcel of land you are going on the CROW access maps and legal closure dates are listed there. I searched "Open Access Natural England" and their map search page was top of the list (duckduckgo search).
And I had a look at a couple of Nidderdale areas, everything I looked at had restrictions - no dogs except guide/assistance dogs. Other than that no closures. That doesn't mean you won't be challenged, it means you have a legal right to be there (sans dog).
They don’t tend to officially close the moors for shooting - odd days here and there mid season would be an easy give away to sabs. Easier to just go ahead and shoot, and if a member of the public unknowingly so happens to be there then they can be redirected somewhere more convenient by their burly, gun totting appearance.