Comets also have frozen carbon dioxide, methane, ammonia, and a few other chemicals. Third, snow is too dense. Comets are delicate, gossamer objects. Cometary material makes snow look like lead. These things are saturated with carbon and silicates, making them as black as tar.
Cometary material is a little like that.
Most of the time, comets spend their time in the supercold outer reaches of the solar system. Out there, they are frozen solid, inert and unchanging. But when one enters the inner solar system, sunlight starts to work it over, heating it and vaporizing the ice on the surface. A good tail can be ten million kilometers long, at least. The comet doesn't have the gravity to hang on to most of them, so they keep drifting, entering orbits around the Sun that are similar to the comet's orbit.