You'd think that's an easy task in 2013. The truth: not so much. The native Android mail app did add it easily (using POP3 I assume) but the app never received a single new message since setup. I tried adjust every setting that seems relevant and nothing made any difference. So it's time to crowd source online. It didn't take long for me to find this post by John Law. That seems to make sense, but my dear wife doesn't want to sync contacts from Hotmail. I thought since it's about the underlying sync protocol - using ActiveSync - so why not just set up the email account with that option. So I did. On the email setup screen select Other (I think Corporate works too), enter account credentials, then click "Manual Setup". From the choices select "Microsoft ActiveSync". Information then actually gets filled in automatically for you: server is m.hotmail.com as mentioned by John Law, and username is an awkward \firstname.lastname@example.org, which I left alone, since I have no clue on what the domain can be. After that just follow along with the Next buttons, and everything started working once it's done!
A side note is that the Hotmail account was not long ago migrated to outlook.com (as required). Maybe that change resulted in some underlying shift, which broke the old scheme.