Organisms on Earth have evolved many ways of spreading themselves to other environments suitable for them. Palm trees, seen on the beaches of even the most isolated islands, have a large seed that floats in the ocean quite well for very long periods. There are countless other examples.

Each of these adaptations survived because there were many receptive environments for the trick to work on. If the ocean wasn't full of coastlines with sandy beaches, the coconut gimmick wouldn't do much good.

It seems like a very remote possibility that an Earth-evolved organism could create an adaptation to spread itself across space from a planet. The mechanisms involved would be complex, and the slim likelihood of another environment suitable for it out there would ensure that the adaptation would die out on one planet anyway. Larry Niven postulated "stage trees," enormous vertical towers that were essentially natural multistage solid rocket motors that fired a space-resistant seed to escape velocity. However, in the story, it was assumed that these were genetically engineered. To have such a thing evolve naturally would be almost impossible, unless something started out by using such a mechanism to spread its seeds across a planet's surface.

But now, lets look at another environment. I'm hearing that more and more gas-giant moons are being found to have possible underground oceans. Maybe ice moons with subsurface oceans in the solar system are the rule instead of the exception?

If something evolved on such a moon, could it come up with an adaptation that would allow it to spread to other such moons, especially in the same gas giant system? Escape velocity from a small moon is relatively low, particularly if you aren't interested in actually leaving the gas giant system (much higher escape velocity). Perhaps some of the geysers or volcanoes can get some of their materials permanently away from the moon into the orbit of the gas giant, where it can reach other moons?

No "stage tree" required. Maybe all you need is a near-immortal spore form that can resist radiation and vacuum long enough to land on another ice moon and slowly be subducted down into the ice and the oceans below. Such a form might have already evolved on a moon to allow a life form to survive long freezing episodes, or to spread itself across the moon from geysers that don't reach escape velocity.

Just some random thoughts. I haven't thrown any numbers at this at all.

Things to look for:

"Ring" clouds in the same orbit as an ice moon, indicating that elements from the moon can attain escape velocity from geysers or other occurrences.

And of course, if we do find life on one moon, look for the same stuff in other places.