No, certainly not from a planning perspective anyway. Unless they are full time working agricultural horses ie pulling ploughs all day, thats the only exemption.
Many councils require change of use for agric fields to be used for horses grazing because of this but this is more of a grey area, depending on whether the horses are fed supplementary feed and whether any structures are put up like shelters etc.
It depends which law you are talking about. They are classed as such under a lot of animal health law which comes from Europe, because they are commonly eaten over there. Do you have a particular area of law in mind?
Probably means that they don't want horses, although a horse grazing in a field does not need any permission in planning terms. Normally land for grazing is advertised as "grass keep" and is for a limited period, generally 10 months of the year. Land available to rent for agricultural use might mean arable land for crops of one sort or another. It also depends on who the owner is, it might be a charity or a trust and the details of the letting are important.
Best thing is to telephone the advertiser and find out.
Sometimes you do need PP for grazing.....just look at the recent furore in the New Forest for starters!
The following is from H&H equestrian lawyer response to a reader q on this subject:
'The use of land for grazing horses does not require planning permission provided the majority of the animal's food is obtained from the land.
This is considered to be an agricultural use of the land. However, if the grazing is part of a commercial activity, such as livery, this will require planning permission.
If horses are turned out on the land for exercise and the grazing is incidental to keeping them on land as opposed to grazing them it is not considered to be an agricultural use and will require planning permission for change of use. '