The approach posted by Michael Karas with several 2x4 arranged to create a channel down the middle makes sense in terms of the structural post for your project. Fastening several smaller pieces of pressure treated lumber together should alleviate the extreme warp/twist you can get with using a single larger post, and by not machining the channel, you're preserving the integrity of the pressure treatment process. I did want to post a separate answer though to address some additional points:
First, this should go without saying, but if the post is in contact with the ground, it should be constructed from ground-contact rated pressure treated lumber, not lumber meant for above-ground use.
Second, based on this quote from your question:
and covering up the dado with "ornamental" wood tacked to all four sides
The typical approach to trim a rough post would be to build a sleeve-like box with your trim wood, and install it semi-floating - slide it down over the post and tack it on to the post along one side only. The sleeve should be built to fit loose on the post, not to the exact dimensions of the post. This prevents warp/twist/checking/shrinkage in the post from causing your trim joints to pop or misalign down the road - the post can move (somewhat) freely inside the trim "box" without disturbing it. Your light fixture or other trim on the top of your lamp post would be attached to the trim sleeve, not directly to the post.
That approach is superior to the literal explanation you gave in your question, of tacking trim to each side of the post, which pretty much guarantees that you'll end up with an ugly trim job down the road as the post moves/shrinks differently than the trim wood.