The unicorns make their debut frolicking in the flower fields and open - air temples of ancient Greece along with their friends, the satyrs, playing and generally having a good time. They also engage in Bacchus' celebration along with the satyrs, centaurs, and centaurettes, enjoying the dancing and wine making.
Soon, their fun is spoiled when Zeus decides to create a thunderstorm with powerful winds and heavy rain, forcing them (along with the rest of the surface dwellers) to take refuge inside temples, groves, and hedges before he can unleash his thunderbolts. When he tires of tormenting them and goes back to sleep they celebrate the storm's end along with the other creatures and enjoy watching Iris casting a rainbow over the sky with her cape, Apollo racing away on his sun chariot and waving goodbye to them as the sun sets, and tucking themselves in as Morpheus casts her cloak of night over the land. By the time Diana shoots her arrow into the sky and fills it with stars, they are sound asleep, as is everyone else.
In Once Upon a Time, Maleficent owned a black pet unicorn. She and Regina duel over the Dark Curse and when Regina tries to kill Maleficent's unicorn, Maleficent shields it with her staff, protecting it, but losing the Dark Curse in the process.
After Snow White and Prince Charming learn of their unborn child's potential for great darkness, they learn that if they touch a unicorn's horn, they can glimpse what their child will be like in the future. When Charming touches it, he see's a young baby in the forest but when Snow touches it, she sees her teenage daughter rip her heart out and crush it.
They don't seem to exhibit a lot of variety in colors as do the Pegasi Siblings, as they're only shown as white with pink manes or blue or pink with white manes. They all have golden horns, however.
They're somewhat close to classical representations of unicorns, having hairy fetlocks, spiraled horns, a "lion" tail, and cloven hooves.
They seem to get along well enough with the centaurs to the point that a centaurette took it upon herself to rescue a stranded unicorn in the middle of the storm.
They're not shown interacting with the pegasi, but they are doing so alongside the satyrs, centaurs, and Bacchus.
They are shown to be rather brave. A pink adult (unclear if it was a male or female) was shown braving the storm's strong winds while three babies were hiding under it, though it's not known if it was their parent or an unrelated adult.
Jacchus is a parody of the pretty pastel unicorns; he's a rather unattractive donkey whose only indication of being anywhere close to them is the long yellow horn growing out of his head.