we suddenly discovered that snapping doesn't work in either drawing or edit toolbars when using IE10. We are currently using 3.7, but doesn't seem to work with 3.8 either when trying that. I then tried using the official samples, and they seem to have the same problem.
I am facing the similiar issue and I did manage to find out later that it was a known issue with IE10 and above.. But to my luck my client is using IE9 as of now. But hoping they might upgrade in the near future and ESRI releases the fix by then.