The snowflakes are six pointed stars, or hexagons. Yet, when water freezes on a flat surface, it forms dendrites of feathery patterns-why not hexagonal crystals?
To start with, a frozen drop of water is bound to look different from a frozen film of water, right?
The dendrites are actually trying to do the same thing, they’re producing the same branches you can see in some of those pictures, but the conditions under which they’re doing it introduce assymetries and steric blocks that do not exist mid-air. In less-syllabic words, “a snowflake forming in mid-air doesn’t run into other flakes or into an edge”.
This site shows that, while there are hexagonal features of almost all snowflakes, some don’t look anything like the hexagonal flakes we think of.
It also has a lot of pictures of frost and how frost develops.
Or, maybe, mostly not. (Most of the article is paywalled, but the opening paragraphs are free and relevant, and I think you can get the rest for free by registering.)
Still, you are probably right that snow crystals are systematically different from ice crystals forming on a window. After all, one is forming in mid-air, nucleating on itself, and equally free to grow in all directions, and the other is forming and nucleating on a surface, which will provide a structured substrate for the crystals to grow on, but constrains it from growing in certain directions.