Access restrictions under CRoW sometimes apply, these vary each year - see signing at access points, or check the PDNP website for closure dates.
2023 published closure dates are: - August 14th - 18th ,21st - 25th, 29th 31st; September 1st, 4th-8th, 11th - 15th, 18th - 21st
Open access land, designated under the Countryside & Rights of Way Act (2000) give area access rather than linear access as provided by public rights of way. It also gives a legal right of access specifically for climbing, as well as walking and other quiet recreation on foot.
Please bear in mind however that the landowner still has the right to restrict access for up to 28 days per year (often used on public safety grounds for shooting in moorland areas), and can also apply for longer term restrictions with Natural England (such as bans on dogs, or regular restrictions during particular times of year). It is important to check for these restrictions regularly as they can be added at short notice – all details for open access land in England can be found on Natural England’s website.