The initial release of WebAssembly won't have any support for well-integrated runtimes, which complicates support for any language that isn't C or C++ or Rust. Theoretically you could probably ship the Go runtime with each webpage, but I don't know how you'd interact with the DOM from there.
Well DOM _(from my limited queries)_ is a bit further out anyway. On their design page, DOM and GC are actually lumped together[1]. That being said, i really want DOM access from Rust, so perhaps it's a moot point heh
Interacting with the DOM from C++ or Rust via an opaque handle seems relatively straightforward compared to designing one-size-fits-all GC primitives that will enable multiple GCs to seamlessly interact (because remember, you may very well want code written in Go and Python and Javascript all on the same page, and they'll all want to manage the same DOM).