It’s a common belief that no two snowflakes are the same, and in a way this is true. No snowflake can ever be completely identical to another, because when you get down to the molecular level they will have slightly different kinds of water molecules, different electrons and different traces of other materials such as specks of dust.
However, if we’re talking only about the appearance and shape of a snowflake, then yes it is possible that some will have duplicates. Snow crystals can vary from fairly simple, hexagonal structures to the more complex and delicate shapes that we commonly think of as snowflakes.
The simple flakes have far fewer molecules than their larger cousins and so it’s entirely possible that you could find two that appeared identical when viewed through a microscope. The more complex structures, however, can have more than a hundred different features and each feature can form in a number of different ways. This makes it highly unlikely that you would ever find two large snowflakes that looked the same – but you could have fun trying!
For a more detailed explanation of the science behind the forming of snowflakes, check out this video