Unicorns are an entirely (or nearly) male race that breeds with other hoofed, mammalian quadrupeds. They are also intelligent and highly magical.
Unicorns have no hands, and thus have an effective DEX of 3 for anything that would require hands. They still have a normal DEX score, though, for use in combat and in spell casting.
All Unicorns are Wizards, and they carry their foci with them; their horns serve as permanently enchanted foci, and this property stays with the horn even after the Unicorn is dead, making Unicorn hunting a profitable (if dangerous) profession. Unicorn horns are also weapons that do 2D6 plus CHA (though this effect ends when the Unicorn dies).
When Unicorns are born, they are indistinguishable from any normal male of their mother's species. When they reach adolescence (at whatever age is appropriate for the mother's species), their intelligence jumps dramatically, and they develop the ability to project their thoughts (as words) into the minds of other beings. Since they usually have no words to use at that point, this is generally unpleasant for everyone in the vicinity. Adult Unicorns try to be on the lookout for such things, so that they can adopt (kidnap) the youngster and teach him how to be a Unicorn. Newly awakened Unicorns know no spells.
At the same time as their minds wake up, Unicorns begin to look like Unicorns, though their horns are usually not fully grown for nearly another year.
Since Unicorns have no hands, there are some aspects of their own care that they simply cannot perform. Unicorns frequently adopt (or kidnap, or enslave, depending on your point of view) young women to serve these functions. Contrary to legend, while Unicorns are VERY possessive of their human (-oid) wards, they really could not care less about their wards sex lives.