Maybe distaste for butchery is one of the reasons dwarves are not traditionally ranchers. It is only the moment of death that bothers people, coming into the room seconds later to find chunks everywhere doesn't bother them at all. There is no glory and little skill in killing a trusting, friendly animal that isn't even fighting back. It just isn't very dwarfish.
They really don't seem set up well for raising livestock in an organized way. Dogs and cats are well integrated into the village, but horses, cows and other large animals just wander around aimlessly and get in the way. You can keep them as livestock, but dwarfs are bad at it in a variety of ways. They either leave the horses wandering around the caves loose, tie them up one at a time, attempt to lock them in a room, or cram way too many of them into cages. Despite all their craft skill dwarfs have still not invented the corral. Feeding the livestock and cleaning/harvesting the dung isn't mentioned at all. If you keep them in outdoor pastures then it could make sense that they need almost no care, but if you lock them in cages deep underground or allow them to congregate in meeting halls, then it is very odd. It would be nice if animals that eat grass had a natural preference for being outside. Having dogs congregate at the well can be useful, but stray horses and cows are just a nuisance.
Butchering animals doesn't seem to give a very strong negative "seen death" thought. I recently slaughtered a good chunk of my out of control horse population, and I checked on the butchers periodically to make sure none of them were getting too unhappy. To my surprise all of them were at least "content", many were "happy" and one one of them was "ecstatic" despite every one of them having the "seen death" thought.
Things that may help:
-- I give many dwarves the butchery job, so one guy doesn't have to do it all the time.
-- I check the individual preferences, and disable butchery for anyone that has a preference for dogs, cats, horses, mules, cows, or any other animal that I plan on farming. I don't know if it makes a difference or not, but I assume that someone who really loves cats will be more upset by killing cats than someone who is indifferent to them would be.
-- I keep all of my indoor workshops, including the butchery, in enclosed rooms. The rooms are usually 7*6 or 9*6, and each contains two workshops and some storage space. This is mainly to contain or slow down miasmas, invaders, berserk and tantruming dwarves, but it also means that usually no one but the butcher sees the moment of death.