No two snowflakes are alike? How can we know that? No two thumbprints are alike? I guess so. What about eyeprints?

It is not that "no two are alike" ... but the odds of witnessing such a thing is so large, that it is the same as true.
It's like saying you'll never be hit by lightning.  Sure, people are hit by lightning every year, but the odds of it happening to any specific person is so low as to be "never happen".

Yes - there are identical fingerprints.  Until one of them gets a papercut (for instance).
I don't know about retina "prints".

And I guess it would be possible for two people to have the same "facial recognition" features.
Especially with modern facial reconstruction surgery.

Interesting:

The exact form each snow crystal takes depends heavily on tiny changes in temperature and humidity it encounters as it falls, resulting in extraordinary diversity.

"It is probably safe to say that the possible number of snow crystal shapes exceeds the estimated number of atoms in the known universe," Nelson said.

Still, while "no two snowflakes are alike" might hold true for larger snowflakes, Nelson figures it might ring false for smaller crystals that sometimes fall before they have a chance to fully develop.

"How likely is it that two snowflakes are alike? Very likely if we define alike to mean that we would have trouble distinguishing them under a microscope and if we include the crystals that hardly develop beyond the prism stage—that is, the smallest snow crystals," Nelson said.

"Good luck finding them though," he added. "Even if there were only a million crystals and you could compare each possible pair once per second—that is, very fast—then to compare them all would take you about a hundred thousand years."

https://www.nbcnews.com/id/16759121/ns/technology_and_science-science/t/two-snowflakes-may-actually-be-alike/#.XOWbzYhKiUk

Also interesting:

https://www.m2sys.com/blog/biometric-hardware/iris-recognition-vs-retina-scanning-what-are-the-differences/