Beale (or is it Beagle...?): Beagling is hares, and is done on foot, though I think it does have the "pink" jackets. The senseless slaughter you're thinking of uses foxhounds.
Foxes are a real pain if you keep free-range poultry (as I do), but why kill them if not?
Vogelman:
A red fox the same or very like the European one (which is Vulpes vulpes) does occur in N America, & no doubt it does similar bloodcurdling screaming and yapping at night as ours do here in the UK. It sounds much like someone murdering a smallish dog very nastily.
I can't say what else might make night sounds in the US, as most other species are different from here, but possibilities might include owls, whippoorwill, nighthawk or other nightjars, or perhaps other mammals (coyote, skunk, *******, martens...?). 12 owls to choose from! There are only 7 or so in the whole of the UK.
You probably do have barn owl (Tyto alba) as this species is almost world-wide. It's sometimes called screech owl here, but I don't think it's the same as the American screech owl. Barn owl makes unearthly groaning and wheezing noises, usually at dusk, but perhaps not loud enough to wake the family.