Black body (or black body radiation) is a term introduced by physicists in the 19th century, to describe the thermal radiation emitted by a body. The intensity and spectrum of such a radiation is only dependent on the temperature of the body.
The term "black" is to denote the idealized case where the body is opaque (i.e. non-reflective) in all the frequencies of the electromagnetic spectrum.
Even though snow is highly reflective in the visible part of the spectrum, it can be idealized as a "black" (or opaque) body in the infra-red part of the electromagnetic spectrum, only absorbing and emitting radiation, but not reflecting.
To wrap it up, snow is a black body in a thermal-radiation-sense, not in a visible-light-sense.
Technically, a black body absorbs all the electromagnetic energy impinging on it. This is obvious incorrect for snow in the visible portion of the electromagnetic spectrum, but snow in the infrared portion of the electromagnetic spectrum is a "good" absorber (Please see link below.) and so snow is referred to as a black body in infrared. This "nominclature" also applies to paint.