When migrating assets, you are migrating the actual base asset that was imported into that game when it was created, however these assets are just the “default Look” assets, once an asset is placed into the world, it’s material setting can be modified for how they want things too look in the game ( Cave). The ones you see without snow in the cave demo are the same assets, might be using a totally different material setup.
Short story here is you can only migrate from the Content Browser, which stores the default look for each asset, and they were then edited to suit their needs for a specific area of the scene., everything you see in the level it’s self was made using the assets from the content browser, but all the pieces necessary to re-create are there after migration.
You can go back and click on the rocks in the scene, and find our what material they used there, so I’m sorry if that wasn’t clear last time, but when you copy all of the assets, you have everything you need to make a scene like that, but you do not get any assets that are in the scene, just the base assets from the content browser used to create the scene.
But with all the stuff you now have, you can recreate it, just comes down to getting the right materials, set on the mesh, ect. 