Minecraft block durability

It's not possible for snow to exist on slabs/half steps. A slab is only ½ blocks high, but as far as the game is concerned, it inhabits an entire block. The same goes for the snow layer, which is also a block — except other blocks you place can go through and replace the snow layer block. So snow on a slab would have to float half a block above ground.

Try placing a cobblestone block on a slab, same thing:

Double slabs are a different block entirely. Their height is exactly one block, so snow can exist/will fall on it.

Edit to add:

Are there any solid blocks that snow cannot stick to?

Those would be non-opaque blocks: Glass and ice. In Fancy Graphics mode, snow will also not fall on leaves.

Resource packs will only replace the graphics (and presumably sound effects) of the resources they are overriding. Everything else will, in general, default to their vanilla graphics. I have often used an HD vanilla texture pack in a modded environment. The contrast between what is replaced and what is not is not really that big of a deal unless the texture pack is a drastic change from general minecraft appearance.