The weather stuff shouldn’t be too hard, set up various particle systems and materials that are affected by the same blueprint that can control wind and all that stuff you need.
The building part is doable with blueprints.
If you want trees to grow you can’t use the foliage mode, instead use Blueprints. Also, unlike what Sirhope says, it’s doable with speedtrees as long as you don’t use foliage mode. Just because there isn’t a built in feature in Speedtree doesn’t mean it’s not doable. There is no difference between a speedtree and any other static mesh, so anything you can do with a static mesh you can do with a Speedtree. just make a whole tree, a stump and a tree with the bottom missing, then switch the meshes with a blueprint when you “cut” them and make the tree fall or something similar. The same goes for having growth, just make a couple of various stages of growth that switches over time using blueprints.
When it comes to changing the landscape you’ll have a harder time to accomplish that. You’d need some kind of voxel system I guess to do that, it have been done so it’s certainly not impossible, but it won’t be easy. I think someone implemented PolyVox into UE4.