I am wondering if it is okay to mix armors in the game? I mainly use heavy with a hood instead of a helmet but when doing Dark brotherhood missions I like to wear the light armor from them. Is that okay to do? Does anyone else do this? Do I need to spec into a certain armor type or can I continue to use both?
While it is perfectly fine to mix armor types, there are some elements in the game intented to make you identify with one type over the other.
To make a good armor selection decision, there is much to consider:
Consider the primary attributes of armor: armor rating and weight. Rating is why you want armor. It reduces physical damage taken. Weight is a big obstacle (less loot, less weapons, less potions). If you go without a helmet, you don't get armor rating from that slot. How much armor rating do you lose by that choice? Does the weight reduction (and magic bonus) make up for that? Can you compensate for the armor rating loss with an alteration spell?
Consider the secondary effects of armor: reduced movement, increased staggering, increased noise. Do you have ways to compensate for those problems? Are you prepared to trade away armor rating to solve those problems instead?
A good player can see the three paths (caster, light, heavy), see how the perks lead into those paths, and discern the tradeoffs when straying from those paths. It's fun to leave the obvious paths, but it's not fun to feel ineffective.
There are certain perks that grant additional bonuses when you use all heavy/light armor or all armor of the same type. If you have those perks, then its not advisable to mix your armor. If you do not have any of those perks, there is really no penalty for mixing armor.
update in response to comments
As for deciding between what armor to wear, it depends entirely on your play style.
If you like to sneak around a lot and do not have the perk or the steed stone effect, then wearing heavy armor will penalize your stealth rating.
If you like to wade in, take lots of hits and dish a lot back, wearing a full set of heavy armor will help you last longer.
If you are the caster type and wants lots of magika, then wearing a hood and caster robe of your school of magic will let you cast spells for much longer.
Typically I do not like to mix my armor as I tend to go for a particular perk tree when I level up. The number of perks in the game is limited so it'll be a waste to put perks into both trees.
Skyrim is not a game you have to "win", esp. not on the first go-through in the first week after release. As the other answers indicate, there are many variables at work there and no one has played long enough to really say what's best or not, although the David B's answer is very good and demonstrates how experienced players can approach the mini-game of skill and perk selection.
My approach was to think about the character I wanted to try first: a warrior that can heal himself and can make potions, magic armor, and magic weapons. I chose to wear heavy armor because it seemed (after 1 hour) that making heavy armor was more lucrative. I've been happy with that choice. My next character will be totally different.
It seems like you like the light armor/robe approach but there is certainly nothing wrong with using heavy stuff if you think the situation warrants or just find a really great pair of dwarven gauntlets or whatever that will serve you well for at a few levels or until you can sell them.
Feeling ineffective is not fun, I agree, but there always the difficulty slider for those situations that just seem impossible. Save often.
Another observation: you don't have to spend your perk points right away or spend them on the things you think you do most. You can play for a good long while and then select perks based on what seems to be the most needful or interesting instead of what happens to open up.
Finally, if you do find yourself gimped in some fun-crushing way and you don't want to start afresh or from an early save, you can tweak almost everything about your character using the console commands. Yeah, you're meta-gaming, but it isn't like anyone is keeping score (Steam accomplishments notwithstanding).
Have fun and don't worry. Ohmi
I'm afraid a lot of people has gotten things very wrong. If you mix armor both skills increase at the same time but at a slower rate. And since Skyrim, in contrast to Morrowind/Oblivion, doesn't level you up at every 10th skill level you get less "XP towards a new level" the lower the skill is. So leveling both heavy and light armor at the same time should level you up slower, which might actually be beneficial since your attacking skills will be able to out-level you.
Hope that helps everyone!
Heavy armor has an unseen sneak penalty. I'm unsure whether this is applied based on weight or an automatic flag. Sneaking directly towards a guard in full heavy armor (even with a decent amount of perks put into the sneak tree) will only work for roughly half the distance you would travel unseen than if you were wearing light armor with the same perks. I personally like to build a character who has a feasible (In my opinion) reason to join and complete quest lines correlating to the major factions/guilds in Skyrim. This can be difficult because attempting to make a hybrid class that has proficiency in the broad range of skills required to, for example sneak into Blackreach unseen and then continue to run carelessly towards enemies wielding a melee weapon or spell/s, uncaring of my magic or health, well it's asking a lot from on character with a finite amount of perks to spend. At level 81 however you can build a character who is somewhat capable of doing this, without having to worry about something like if you were wearing a full set of same class armor with the applicable perks to boost armor rating for doing so.
A combination of enchantments i.e. magic cost reduction, resistances, melee damage boosting, stat regen and or straight up boosts ect. And an understanding of game mechanics and how they work, for example striking speed whilst dual wielding and whether or not you want to sacrifice the speed of a power attack whilst wielding a sword in main hand and a dagger offhand, for the personal preference of dual wielding daggers (Power attacks with dual wield daggers is actually longer).
It all really comes down to what level and or number of quests completed you want to reach. Because there is no point going into Skyrim straight off the bat with the intention of "Finishing the game" without the understanding that at some point, a line has to be drawn before you enter into the realm of abusing game mechanics just to level or win fights and actually getting you character to a point where, even though the game is maybe far from finished, you could quite happily say that character's story is done.
Want to try something different after that? Sure why not. Want to keep going and see how far you drag the build out? Up to you. Want to spam sneak attacks on Rolof as soon as you get a dagger in your hands? Your choice buddy, hell at that rate, just get sneak 100, play around with light armor and one handed until you reach level 15, if sneak hasn't already got you there, grab the Ohgma Infinium, buy Breezehome, proceed to duplicate. Bam, Level 81 in a couple of hours.
What all of this amount to.... Do whatever want.... it's an RPG after all.