Entropy is not due to the equations of our universe, but rather the initial conditions. So the asymmetry might be apparent but the equations might still be symmetric. Related is the idea of spontaneous symmetry breaking.

Of course, we don't have time symmetry in the equations anyway because of the weak force. But because the weak force is weak//doesn't matter much for the physics of many systems, we can often write the equations of physics as a time-symmetric term which essentially decides the motion plus a very small time-asymmetric term. So we can deal with the small term using techniques like perturbation theory, and use time symmetry for the rest.

Even if it is true in theory, it is not practically true, as the information required to reverse such a transform rapidly exceeds what you can collect even in theory in a single coherent system. While this is by no means the end of your problems, one simple question you can ask yourself is how exactly you intend to re-collect the photons that the snowflake emitted while melting as they head off to the ends of the universe at light speed?

If the universe is externally a pure value, it doesn't matter to us on the inside. The universe is impure from our point of view.

Also, a pure data structure doesn't just imply that you have a puddle of water that you can put back together into a snowflake; it practically (that is, in practice, not in the colloquial sense of the term) implies that you have both at the same time. When I'm working with pure data structures I don't have to laboriously translate back and forth, I have them both in hand. This is partially because pure data structures simply have no concept of time at all in them. And you can't save this argument by claiming you can transform them back and forth at will, because as I mentioned, no, you can not. Common sense can be clad with solid mathematical arguments here; you can not, in our real universe, ever do that, so even the superficially appealing theoretical answer must give way to a more sophisticated and correct theoretical analysis in which in fact you can't reverse arbitrary transforms in practice. (You can do it at a small scale for small numbers of qubits. You can do it for a constrained number of qubits specially set up and isolated for just such an occasion, aka "quantum computer".... and note how hard even that is, we've still not managed to isolate very many qubits at a time that way! But you can not do it in general.)

Whether an entity external to our universe could do it is something you'd have to take up with them.