I've played Skyrim a whole lot, many times. And as I've gotten more familiar with the landscape I've simply stopped exploring. I see the location marker icon on the compass and I know what it is. But on my current playthrough I tried turning the HUD off. It turned I couldn't cope without the crosshair and health bar so I stuck a piece of cardboard over the compass... and my god it's almost like the game is new and fresh. It's made a huge difference. I immediately found myself exploring again, and when I find something I'm like "Ohh what's that."

So I would really recommend giving it a try and covering up the compass.

Such a small and simple thing but it makes such a huge difference. It amazes me the developers don't allow the HUD markers to be toggled off. They have robbed us of the joy of exploration and discovery because of their intransigence and insistence that it remains. Think of all the things they've added to the game since it's initial release, but they never relented and allowed those things to be toggled off.

Quote me if I'm wrong, but isn't there an option to lower the opacity of the compass in TES: Skyrim?

I haven't gotten around to checking for it in a while, but I remember doing something very similar after completion of the main quest line to do some random exploring.

I can't see it making that much of a difference for me personally.

You can turn down the opacity of the whole HUD not just the compass.