I would draw up a contract for renting based on 364days of the year - as in not a full year, otherwise you may end up with the horse on there forever, and you may want to use the paddock yourself at some point for livestock, which may not be possible with a horse on it already. And as other have said .- include in the contract repairs and maintenance costs (a horse out in winter can totally destroy the paddock depending on the type of soil, type of horse and the weather of course), who mows/tops the field, poo-picking etc etc.
TBH - sheep would take better care of the field... but then I am not a horsey person.