In the hobby of animal fancy, the down hair is collectively called the undercoat and may be important in judging the animal, particularly at conformation dog shows and cat shows.
http://en.wikipedia.org/wiki/Undercoat

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undercoat. the fine hairs of an animal's coat which are usually shorter and more numerous than the coarse guard hairs. In some breeds of dogs and cats, however, these may ...
http://medical-dictionary.thefreedictionary.com/undercoat

noun. Obsolete a coat worn under another; an under layer of short hair in an animal's coat; a coating as of tarlike material applied to the exposed underside of a motor vehicle to ...
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