Not TouchWiz (that's just the launcher overlay), but the stock E-Mail app. And yes, it syncs everything with MS Exchange, just add the account from your Account settings and select what to sync and what not to.
This method is ok but it is missing a couple of functions. The mini today cannot be expanded to full screen/4x4 widget so that hinders the usefulness.OK, first things first. When you set up your Exchange account, in the stock Calendar app, can you see your To-Do List items? If you do, then you're OK in the sync department.
Now, as for the widgets, you're right, there's no dedicated widget just for To-Do lists, but if you use the S-Planner (mini today) widget, your To-Do items will appear there.
You could also try a different Calendar app that has To-Do list widgets, too.