First; I believe switching to master difficulty later in the game is not playing the game on master difficulty.
Before crafting my strategy on my most recent character, I considered this; the enemies of this game have different levels. If you are a level 3, you will not be able to beat a level 12 enemy. The skill, health, mana, stamina, etc. level differences are too high to overcome. My conclusion was I had to choose my path carefully; deciding whether or not to enter a cave or log it and return another time, finding quests that were appropriate for my level (Whiterun area's bounty quests send you to appropriate level caves). A warrior of Skyrim chooses his battles carefully, retreats when he is overcome, and never forgets anything.
Even if you choose the right battles, without a proper strategy you will lose. Dragons, mages, bears, sabretooth tigers, gangs of bandit champions, and a frost troll on the mountain leading to the graybeards are all enemies to consider. How can you craft a character that can defend and attack such diverse enemy builds? I have made over a dozen characters so far, and none have been able to be successful beyond the whiterun plains. I did defeat the frost troll and a sabrecat with my last failed character, but his level and skill progression were being hobbled because of my companion Lydia. I could not have defeated those enemies without her. She limited my skill usage, which limited my skill progression. For fun, I think I'll have her with me whenever I have a quest that involves allied npcs; the more the merrier.
My skill set includes warrior skills (one handed, block, heavy armor, and armorer), thief skills (archery, sneak, lockpick), and mage skills (destruction, restoration, conjuration, enchantment, and alchemy), and he is a Breton for the magic resistance. I decided to include so many skills because of enemy level progression relative to mine. I believe as my level changes, the enemies do not grow stronger, so I can increase lots of skills and level up quickly without enemies becoming invincible. My strategy is to level up as much as possible.
I won't go further than this, because this post is long enough, but these are things I feel are necessary to consider in order to have any success on master difficulty. My current character is getting ready to leave his home at Whiterun to pursue new adventures, and I think he's going to falkreath. I haven't even discussed combat strategy, economy, alchemy management, etc., but if anyone would like to, I would be happy to oblige.