A weed is a wild flower growing in the wrong place.
In the UK we have ragwort - which is as toxic dead, after being harvested as it is found growing alive. Luckily horses won't choose to eat it, if given the choice of other plants to consume. The danger comes if a horse is hungry because other vegetation is lacking through drought or over grazing.
Grass is a subject all by itself - there are thousands of different varieties, the majority of which are safe for a horse to eat. Some grasses are more nutritious than others.
It is a good idea to know which toxic plants are likely to be found in your area so that you can learn to recognise them. For advice ask the local vet, the local farmer and consult the local branch of the regional horse society.
Over here we have tendency to repeatedly use the same hay supplier whom we can trust to be selective in which fields they use to grow grass for hay making. A big danger for Brits are the hedgerows which can be a thousand years old in which thrive some plants dangerous to horses such as yew and deadly nightshade.
Grass husbandry and hay production is a subject worth studying by horse owners. Poor hay can be a source of sickness for horses. Ideally soils on which horses graze should be tested yearly and re-balanced with fresh seed or other treatments where necessary. Pastures used for horses should be rotated for grazing by other herbivores - particularly sheep. Horses are harsh users of grass fields - they scuff it up with their hooves, they selectively graze, they defecate on it and thereby alter the PH.
We horse owners pay a lot of attention to training our horses and we pay out lots of money for additives and fancy treatments but often we don't watch the quality of the grass the horse eats - partly because often the management of the grass is not within our control.
Ideally - all dung should be collected. The soil tested for ph. The field should be harrowed at least once a year. Certain weeds should be eradicated. A watch kept for notably poisonous plants which should be dug up and burned. Sick or potentially sick animals should be confined away from healthy animals. Etc etc etc. So if you have a hay farmer who takes care of his fields, then don't argue about the last few cents of the price per bale.
I know of several farmers who will willingly make and sell hay but who won't have horses on their grassland.
PS When you have finished studying about grass, pick up a text book on water.