What different nuance is it between 'it begins to verb' and 'it is beginning to verb'?
the same problem is in case of 'start'.
Someone else will probably come up with a better answer to this, but to me "it begins to…" is more like you're narrating an event. "it is beginning to…" is more like you're describing an environment.
"It is beginning to…" should work in pretty much any situation, whereas "it begins to…" would sound a bit awkward in some places. For example, if I were driving down the street with someone and they said "it is beginning to snow" I wouldn't think twice (well, "starting" would be a bit more idiomatic than "beginning", but whatever). If, on the other hand, they said "it begins to snow" I'd definitely notice it.
Conversely, if someone were narrating a movie and said "Night falls over the town. It begins to snow." I wouldn't think twice. I also wouldn't think twice if they said "Night falls over the town. It is beginning to snow."