With the came and gone of Christmas, perhaps you've been left in the cold by Santa, with not a new game to be had. Perhaps you've nothing new to play, and Skyrim sits lonely and unplayed on your shelf. No reason to play Skyrim any more, you've already done every thing you could possibly do in that game.
That's where you're wrong!
There is still plenty to do, you just have thought of it, so allow me to think of it for you.
The Milk Drinker
You are a milk drinker. You can't fight, you are easily frightened, and have a strong distaste for germs.
You have to rely on followers to help you though the dangers of Skyrim. You may use your fists in the most dire of situations, but other than that, nothing. No weapons, no magic. You must also maintain an armor rating of 0 for the entire game. So if you can't fight, how are you supposed to get followers to help you? Steal? No, you are a milk drinker, you'd never cross the law. The answer is you do hard honest labor and earn an honest pay. Earn some honest coin by chopping wood, picking crops, mining ore, and gathering plants. Once you have enough money to hire a mercenary, you can go on some more dangerous adventures. With this tough adventurer at your side you can take on any cave or barrow, but it would probably be best to hide in the corner while they do all the fighting. Caves and barrows are dirty and filled with scary things though. Best not to dirty your hands with looking through draugr pockets or old chests, there could be spiders in there. So basically you are restricted from looting any bodies, chest, or any other form of container. What are you supposed to sell then? Well people will often give you weapons or armor you don't want for completing quests, sell that, or give it to your follow to improve their equipment.
No weapons, no armor, no magic, no looting, no stealing. No using any skills other than Speech and Sneak. May use hand-to-hand in an emergency, but rely on followers for combat.
Obviously if you should take a quest that requires an item to be obtained, you may take it to complete the quest. The necklaces Locket of Saint Jiub and Amulet of Articulation are exceptions to the no armor rule, being that they are are neckware and not actual armor. Race powers (such as Battle Cry or Berserker Rage) are not included as "magic" and may be used when felt needed. Theft is allowed in a single instance, which will be gone over later. Coins and coin purses that are left exposed (ie just sitting on top of a table) may be taken, as long as it's not stealing. Any keys that are required to progress obviously may be looted. One Pickaxe and one Woodcutter's Axe may be looted when you see one, simply due to difficulty in finding them from vendors.
As a wealthy Skyrim citizen you need to look the part. You can't go around in those prisoner clothes forever. Your first goal is to acquire a set of average clothing. Any set of normal clothing and footwear will do, and a silver necklace and ring (gemmed is preferred). Now that you look slightly more respectable, you need to get the good clothes. Fine Clothes and Fine Boots, as well as upgrading your jewelry to gold (gemmed is now required). Now you look rich, but you aren't just rich, you got to look richer than everyone else. To insert yourself into the highest caste, you'll need to get you hands on a set of Noble Clothes (which are the sole exception to no theft) or Emperor's Robes and Fur-Lined Boots, as well as a Gold Diamond Ring, Gold Diamond Necklace, and a Gold and Ruby, Silver and Sapphire, or Gold and Emerald Circlet.
You need to create a name for yourself, to this end you need to get into real estate. You need to buy and fully upgrade every house (if you have Hearthfire the manors are included). You'll also need to invest in as many businesses as possible.
Now that you have created your financial empire, you'll need to create an heir. So you must join houses with another family (If you have Hearthfire you can actually adopt an heir, but everyone just pretend like sexy baby time actually works). So you need to marry on of those listed below.
You can't progress past the basic starter equipment. Meaning you can not use anything that can't be crafted at a forge with no perks. You may also not use any spells beyond Novice, and can't use any shout past the first word. Can't wear any "mage robes" past Novice Robes, Novice Hood, Necromancer Robes, or other basic "robes" under 75%. Can not place any perks into smithing or enchanting.
When Daedric equipment has been obtained, it may be worn.
I would like to hear some other's ideas, but remember that all challenge must have a specific goal that is just "complete the game".