Mine already do all that and they aren't interested in having one of their own (they ride a friend's bombproof pony). Its just part of having a family "pet"... even though they can't ride my horse. My lil one prepares feed for all 7 horses in the barn whenever I let her go (too cold or too late on a school night is a no) and all of them have vastly different feeds/meds/soaking requirements.
Older kiddo likes to clean out the pig mare's stall since you just shovel out the entire contents not have to pick through bedding.
They've helped with Vet/Farrier visits. They turn in/out the "child-safe on the ground" horses. They can fix a blanket or remove one (all the child-safe older horses are way too tall for them to put a blanket on).
'Course they also feed the cows, pigs, chickens, turkeys and goats on a daily basis. They've bottle-fed calves whose Mom's died, chased and held down pigs for shots.... pretty much anything that's done around here they're in the midst of. They live here, so they can help!