How does many terrains on scene affect performance?

Terrain in Unity isn't great for performance. This is clearly visible the larger the terrain gets. Splitting it up into smaller pieces is in fact the way some people have tried to improve performance. However, from what I can see, you will have an insanely large amount of these terrains. This might actually be worse than just one terrain piece, simply because of the number of them. This is similar to trying to render one model with 10,000 faces vs 10,000 models with one face each. The larger model is easier to render.

Increasing the terrain chunk size and simply having less of them should improve performance, and only rendering the terrain chunks visible by a camera should again improve performance significantly (occlusion culling).

If this is the way you want to do it, then you should take a look at methods which convert terrain to mesh, as mesh it easier on performance. There are scripts on the internet which can convert terrain objects to mesh, keeping trees and grass orientated. However, the terrain will lose some detail.

I can remember using TerrainObjExporter in the past, but I don't know whether it will work in real time, or only in the editor, so it might not be what you're looking for.