Not All Animals Are Equal, and Some Are More Equal Than Others
In 2018, the federal stalking statute was amended to cover not just threats to "a person" (including the victim, the victim's immediate family member, and the victim's spouse or intimate partner) but also threats to:
"Pet" is defined to mean
a domesticated animal, such as a dog, cat, bird, rodent, fish, turtle, or other animal that is kept for pleasure rather than for commercial purposes.
So horses, alone among animals, are covered regardless of whether they are kept as pets, as service animals, or for emotional support. Even threats to working horses on one's farm are covered by the statute.
(I assume, by the way, that a dog kept for commercial purposes is not covered by the "pet" definition, because the "that is kept for pleasure rather than for commercial purposes" clause covers all the animals, and not just "other animal." I realize there is no comma before the "that is kept for pleasure" clause, but in context that seems like the better reading, given that the term being defined is "pet." Dogs kept by a breeder for sale are domesticated, but not pets, I think.)