The name of the plant only says half of the truth. This plant does not only have toxic effects on dogs but also on horses. More than 30 leaves can cause death.
The Dogbane Family, also called Apocynaceae, is a whole family of plants and stands for more than 4500 species.
Most of these species are Vincas (evergreen shrub) which are really toxic (for humans, dogs and, especially, horses). The shrubby plant can grow up to one meter and all parts of the plant offer toxic substances. They even keep their dangerous and toxic substances in a dried state. If horses eat more than 20-30 leaves this can cause death.
Nerium oleander is one of the most dangerous species of the evergreen shrubs and therefore can also be specified into the Dogbane Family.
Usually it is only called Oleander and it is really popular due to their pretty and colorful flowers (they can be red, white or yellow). Oleander offers a lot of the toxic substance Glykosid Oleandrin so that it is one of the most poisonous plants. Horses can die if they eat 10-20g (about 20 leaves; in opposite to this just one single leaf can be fatal for humans!). The toxic substance Glykosid Oleandrin causes arrhythmia until the heart totally stops to beat. Generally experts advise not to plant Oleander in the garden. Little wounds on hands or feet can be the entry into the body for toxic substances. If you have Oleander in the garden this always is a risk.
In general one needs to control all places where horses are without supervision (e.g. pastures) if there are any poisonous plants.