I was very disappointed with Bethesda taking away our ability to fight underwater, and with it the ability to do lots of neat things under and on the sea. Likewise with the removal of waterwalking. Most of the water in this game is in an arctic region (the Sea of Ghosts), and they expect people to swim in there? Are they nuts? I loved the Jewel of the Rumare in Oblivion, and using it to poke around every underwater area I came across, especially the flooded dungeons. There are a few wrecks you can swim down to in Skyrim, with a few chests to pop open, but that seems to be all. Like Bacillus said, it hardly even seems worth the effort. It seems like they removed a lot of opportunities for fun in the game.
I was also looking for more underwater stuff. There is on location with
underwater. And yes it seems to me that you should be able to swing a weapon underwater. I think Oblivion had it right (maybe Morrowind too as I recall) You can swing a blade or blunt and cast on-touch spells (which don't exist in Skyrim); but could not shoot an arrow or ranged spell underwater.
Miss all of this. Really miss being able to fight underwater. It seems silly that the great Dovakin can fight off mystical dragons...but is a water wimp.
I also miss being able to 1st/3rd person horseback ride (the mod to do this kept crashing my game). AND Morrowind had the best questing I have ever done. You never knew what would happen until it did. Plus in Oblivion horses were cool and served a purpose. In SKyrim they are just too slow and cumbersome. I would rather run/walk. I don't fast travel. I guess I got used to being on foot in Morrowind even with the Striders. I would rather adventure. Which brings us back to where are the underwater adventures? Still all in all a great game and fun.