That road is not far from me, it is mostly straight N/S with some sections overhung with trees. There is a 60mph limit on most of it: although it runs through the New Forest it is fenced, so animals should not be a problem.
That road runs from Cadnam to Brockenhurst through/round Lyndhurst, it looks like the section from Lyndhurst to Cadnam. I was travelling in that area yesterday afternoon, mostly dry roads but with some sudden heavy showers. More on the story at
https://uk.news.yahoo.com/driver-caught-damp-conditions-sports-111333802.html