Those with horses will be more likely to pay more money for the grazing, but they will probably want some sort of shelter and access to a water source. The other worry with horses is the fact that they will poach the ground horribly, especially through the wetter months.
Sheep grazing sits about 25-35p per head per week during the winter, the lack of water will not be such a worry but it will be used as a bargaining point to get a lower price by the grazier.
It may be worth while phoning your local auctioneers (McArtneys of Worcester, Bidwells?) They may have a list of local farmers who normally take on grazing throughout the winter and they could set up a proper commercial deal to ensure that you are legally covered and that your money is assured to be paid.