This is an drawing of the Galileo probe exploring Jupiter's environment.
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Image from: The Jet Propulsion Laboratory
The Atmosphere of Icy Moons
It is unlikely that the icy moons have an atmosphere. The reason they have no atmosphere is because they do not have enough gravity. Gravity depends upon the amount of substance (mass) contained in a body. The smaller the body is the lower its gravity, so moons have much less gravity than a planet has. The icy moons are made of ice, and because ice contains less substance than rock, icy moons have even less gravity than a rocky moon of the same size. Because there is little gravity, an icy moon cannot hold onto an atmosphere for very long.
An atmosphere can come from inside a moon. Some icy moons may have active surfaces, such as Europa, where the surface may "crack" and release molecules for an atmosphere from inside the moon.
However they get there, molecules may float around a moon for a while, but because of the low gravity, whatever "atmosphere" may be created rapidly drifts away.
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