No. Horses are members of the family Equidae. Cows are members
of the family Bovidae. They are also in separate Orders - Cows are
even-toed ungulates like sheep and goats, horses are odd-toed
ungulates like zebras.
No, a horse is part of the equine "family", while a cow (female,
and bull being male) is from the bovine "family".
In this context, family can be considered to be the species.