All extant mammals have hair, at least at some time of their lives. Indeed, hair is one of the synapomorphies (shared derived characters) that define mammals.
These hairs may occur only during early life (in embryos, newborns or juveniles), and then disappear, or be maintained throughout life and present many different types (including the guard hairs, wool, underfur, etc that we know well).
In fact, mammal embryos are often covered with special hair called lanugo that is lost before birth.
Whales do have hair: at least the young of some species have some vibrissae-like hairs on their snout (and even when these hairs are lost, the sensory terminals associated with them remain).
http://animaldiversity.ummz.umich.edu/si…
And naked mole rats have tactile vibrissae too :-)
So at least sensory hairs are present in all mammals, associated with sensory nerve cells and those little muscles, the arrector pili, responsible for hair erection and our goosebumps.
More about mammalian hair:
http://animaldiversity.ummz.umich.edu/si…
BTW you're right about the breastfeeding part: the presence of mammary glands that produce milk for the young is another of the synapomorphies of mammals. However, only marsupials and placental mammals have nipples (monotremes don't).
More about the definition of mammals:
http://answers.yahoo.com/question/index;…
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