I think there are several possibilities. The way I personally imagined it is like:
Step 1- the snowballs are done inside the cloak with bare hands, as muggle/no-maj would do it.
Step 2 - Wingardium Leviosa the snowball to your target.
Alternative way is that Harry did the snowball creation and throwing through the cloak itself. That is, he grabbed the snow near him, with his hands behind the cloak. Then, just throw it at the target.
The first scenario is more likely, as the second one would be a little clumsy when throwing. You could risk the cloak falling off you, but I think it is totally doable.