It's a potential problem to the locals and the planning authority because they think you may be trying to acquire a change of use of the land by stealth - from equestrian use to a mixed use for equestrian and the storage of caravans. That may then lead to an attempt to occupy the caravan for residential use, which may in turn lead to a right to have a domestic dwelling on the site. Although that may not be your intention, it has been done by others before.
The fact you own the land or there is screening does not change the price of fish.
Talk to the planning authority and see what they say about your requirement. You are likely to receive a more sympathetic hearing if the land is not in one of the special categories (National Park or AONB). In these areas, the policies regarding the siting of caravans is more constrained.