The basic answer is, yes. Tranquilizers are even deadly to horses
if they are given an overdose. Some tranquilizers, such as Acepromazine,
lower blood pressure and reduce the horse's heart rate. An overdose
could be deadly as it could lower blood pressure and heart rates
too low. They could be harmful to both horses and humans --
it would just take a larger dose to affect a horse (since their
bodies are larger).
The drugs that are actually used to put a horse to sleep are
Barbiturates (usually in combination with a sedative to calm
the horse first). Barbiturates depress the nervous system, and
they will induce sleep and depress respitory functions and muscle
control, and in a large enough dose (like those given to put
horses down) they induce a coma and death.
Basically, tranquilizers depress body functions, (which makes
the animal tanquil), and an overdose can lower heart rate, brain
function, blood pressure, or respitory rate too low and kill
a horse (or human).
Here is a veterinary
site with more information: http://lam.vet.uga.edu/LAM/LM000084.HTML