You can. How well this works may vary with the asset. You’ll have to just try it and see.
Well, snow in real life isn’t just painting everything white. You may get away with this on some objects or for starters, but if you want more realistic snow you’re going to need to add or change some meshes, particularly on things like grass and trees.
Another way to achieve global changes to your rendering is to use post processing efffects. This might or might not work for you depending on your use case. But if you used a post processing effect, you wouldn’t need to apply your effect shader to every surface.