Same here, guys! I write, after clicking that light bulb on Cortana, then click on the arrow and nothing happens even connected to the internet.
Edit: Hey, no idea why but everything is fine now. I played a bit with the pen, virtual keyboard (reinstalled keyboard language actually) and came back to the handwriting feature. Voila. Don`t ask me what I did to getting it to work. New SP3 user here.
Off-topic, one nice feature I discovered was the personalized handwriting recognition feature for Portuguese, my mother language. Wasn`t there first time I accessed it (I had only the Portuguese keyboard installed at this time). Then I installed the whole Portuguese language pack and thought, ok, maybe I got this now. Nothing. Then I uninstalled the language pack, deleted the Portuguese keyboard, cause in onenote I suddenly couldn`t handwrite using the Portuguese keyboard, and finally reinstalled only the Portuguese keyboard, leaving the English one of course as my main windows language setup. Voila. The personalized handwriting recognition feature appeared and I`m very, very happy, as you can imagine. Even setup a reminder with Cortana handwriting. Good luck guys. Hope this helps.