Installing Tool Progression causes snow to be unbreakable by hand.
Setting snow (layers and blocks) to [email protected] causes snow to be breakable by hand, but always drop snowballs.

Snow is supposed to drop snowballs only when harvested with a shovel.
How would one acheive this while using this mod?

Right now, I'm not able to look into what exactly happens with snow, but based on my understanding, this is not possible right now. I guess, what happens in vanilla is that snow is not harvestable by hand, but has such a low hardness, that it can be broken instantly anyways. However, ToolProgression enforces that you can't break blocks, which aren't harvestable.

If I'd have to suggest a setting, I'd probably go with something along what you posted.
I'll look into it, but this may require a bit of rewriting.

With the upcoming version 1.5.1 you will be able to define a new overwrite or use a global option.