I've tried to play all the way through on Master difficulty but it get a little too hard.
Especially when I have to face 2 Draugr Deathlords and 1 Dragur Scourge at the same time without Lydia or a companion. :\
I think it's best to work up to it. At least, that's what I did. I was on apprentice or adept for quite a while, then tried expert when I thought I had pretty decent weapons and armour plus had increased my attributes of health, stamina or magicka when levelling up. I pretty much alternated each of those with each level up so that I didn't have loads of stamina but little health. Then when I'd improved gear futher and levelled some more, I tried master.
A challenge is important but I think personally you have to balance the right strength of armour, and weapons/spells/stamina/magicka/health (depending on what skills you're focusing on) with the difficulty level, so that it's challenging but not so hard it makes you feel like giving up. But if you're trying to slay dragons, make giants cry or extinguish the lights in draugrs eyes on master difficulty and you have 40 or 50 damage iron toothpicks, low stamina/magicka/health attributes and weak armour, it's going to be quite tough.