Does it matter?
Of that "360 million strong user base" how many of those users are active?
I have a hotmail account, I use it for one thing - spam catching, whenever any online (or offline) service asks for my email address that's the one they get. I don't use it for real email, ever. I check it maybe once a week and if ever I start to get mail into it that I think is important, the sender gets given my real email address.
So the snazzy new design is of no interest to me at all. As hotmail was one of the first wide-spread free web mail services, I expect there are a lot of dormant accounts on it - people set them up there and then moved on to something better over time. Other people probably use it in the same way as I do, and yet more people probably have accounts that were set up there for a laugh (e.g. firstname.lastname@example.org or email@example.com). The only person I know that uses a hotmail account in earnest actually works for MS
So really - does it matter? How many people will really be affected?
PS - I made up those two addresses but will not be surprised even a tiny little bit if it turns out they exist