So every single embark, I end up forgetting to define a pen/pasture for my grazers, and they inevitably end up starving to death, along with whatever livestock the migrants haul along as pets.
It makes no sense. Why would a grazing animal allowed the entire span of the map starve to death with grass under its hooves? How is this a thing? The pen/pasture system is broken. The reason it exists is to make livestock management easier, not more annoying. Having to micromanage pastures just to ensure animals don't starve is downright weird.
Allowing animals to graze free-range is my first and primary suggestion to fix this. I frankly don't care if my wool-carder has to walk halfway across the map to grab a sheep for shearing, even if that puts him in danger, so long as pets aren't randomly starving to death under their owner's noses. Furthermore, animals assigned to a pen or pasture that are running out of food should just hop the fence and run away, like real life. This should be a factor of how domesticated/trained they are - respecting the pasture boundries should be a matter of training or the quality of the fence.
That brings me to my next suggestion. Actual fences and coops. How this would work is some degree of abstraction between taking raw materials like a log and putting down fence posts, to making fence posts in the carpenter and putting down fence posts [personally, I'm in favor of being able to select any material/item, for fences made from stone, leather, meat, spears, arrows, piled skulls, vermin remains, cages with animals inside triggerable by traps, floodgates and windows for absurd whale aquariums, etc.] but it would all rely on the expanding room interface. You select it from the build menu, put its center point anywhere on the map, and + away until you're satisfied with its size. A dwarf simply takes whatever tool or material you're using, and walks the perimeter laying down fence. If they run out of material, they go and fetch more as a new job. More than one person can build the fence, sort of like the engraving job. You can even factor in room quality based on how good the dwarf is at fence building (trapping? would be nice if this skill had some use other than for small animals) and let that and animal size determine how easy it is for penned animals to jump the fence. For elephants, you either need a legend building your fence, or to turn to constructions.
Additionally, you could have an option in the building "room" menu to reenforce a fence later, in case you started out with wood but now have such an abundance of iron that you want to go back and use to make your regular pastures work for your bigger critters.
For chicken coops (or flyers in general, who should need enclosures to avoid running away more than anything else but currently are weirdly the most manageable livestock), they should walk around each tile inside as well, laying grate-like constructions above to represent a cage. Alternatively, the animal handlers/gelders can clip wings.
Doing all this would allow predators, poachers, and carnivorous pets to be a little less serene with your livestock, with much less player intervention than requiring everyone to build impenetrable house-sized walls for animals. It would allow players to balance risk vs. reward for their grazing animals, would make for more reasonable towns instead of having critters bunched up in the city streets, and would also give a reasonable way to cordon off the underground from things like crundles while still making it comparatively dangerous against the building destroyers there.