Hey EternallyBright,
Not bad at all. That seems like a pretty decent basic summation, especially from someone relatively new to the game.
I'm sure it goes without saying, but there are of course times where multiple colours can do things, it's just that one colour does it better than others.
If I may extend upon your descriptions slightly, I'd add the following:
Green - This is most certainly the colour of big mana, but it can achieve this in a variety of ways. It can make use of a lot of mana dorks (such as
Llanowar Elves and
Elvish Mystic), ramp spells (such as
Rampant Growth and
Cultivate) and extra land drops (such as
Azusa, Lost but Seeking and
Oracle of Mul Daya). All of this is with the aim to be ahead of the curve. You hope to have access to 3 mana on turn two, 5 on turn 3 etc. so that you can drop your big dumb fatties like
Craterhoof Behemoth as early as possible.
White - Again, your depiction of white is pretty spot on. It tends to play many small creatures with a view of dropping some Lord or Anthem effects (
Benalish Marshal,
Glorious Anthem) to turn many small creatures into many big creatures and
overwhelm your opponent. It also tends to be the colour of
exile effects, both permanent and temporary (
Path to Exile and
Fiend Hunter are good examples respectively) as well as mass removal, be that creatures (
Wrath of God), enchantments (
Cleansing Meditation) or even lands (
Armageddon). Life gain can also be a prevalent theme here too if that's your thing.
The next three colours are where I personally feel there is a little more explanation to be given. While you were right about everything you said, there are other areas of the colours identities that are worth mentioning.
Blue - This is obviously the colour of counter magic (
counterspell is the classic example), but it is much more than that too. Blue tends to be the colour that cares about tempo. It uses it's mana efficiently and looks to
disrupt it's opponent while it builds towards it's own
game plan. Often this will take the form of counter magic but it can also include much more.
Unsummon is a good example of a blue card that cares about tempo. It doesn't get rid of anything permanently, but it messes with the opponents plan and sets them back at least a turn for just 1 blue mana at instant speed. Unsummoning a big green trampling beast could buy blue enough time to draw into it's win conditions.
Black - My personal favourite colour in MTG. While it does have it's fair share of drain and gain, you are right in saying that that tends to be more prevalent in vampire tribal strategies (though not exclusively for sure). Black is generally the colour that turns whatever it can into resources and advantage. It is very good at killing creatures (both opponents and it's own), and is also very good at turning it's own creatures dying into advantage (see
Blood Artist,
Pitiless Plunderer,
Midnight Reaper,
Harvester of Souls). It also has it's fair share of mass creature removal (
Damnation for example), but cares much less about it's own creatures dying as it can gain advantage from this as described previously, or get those creatures back very easily (
Raise Dead,
Zombify,
Reanimate). But it's not just creatures it looks to use. It will also use it's life total as a resource.
Bolas's Citadel is a perfect example of how black will use it's life total to give itself the upper hand. It also has the sickest art, but that's just my personal preference.
Red - You are absolutely right that red is the colour of direct damage, though I would say that how it gets there is surprisingly nuanced. Mono red aggro decks are often seen as the simplest, cheapest kind of deck, but piloting them is more skilled than you might think at first. There are a lot of decisions to be made when piloting a mono red aggressive type of deck, and there are a lot of strategies that can achieve this. The two biggest are Burn and Red Deck Wins (RDW). Burn tends to try and put a lot of damage on the player immediately using things like
Lightning Bolt and just attacking the opponents life total. Red Deck Wins tends to lean in towards playing many cheap and hasty creatures to
overwhelm the opponent as quickly as possible, and use it's spells to clear the path for it's creatures. It tends to be more robust than the simpler burn, though often slightly slower as a result and a lot trickier to pilot. For example, a common decision for a RDW deck to make is whether or not a
Lightning Bolt is best suited to go straight for the face or to clear a blocker. 3 damage to the face is nice, but clearing that blocker could result in more damage getting through over the course of the game. But generally, it does tend to be balls to the wall, how fast can I kill you kind of stuff. Also, there's Dragons, and who doesn't like Dragons?
And of course there are cards within each of these colours that do nothing like this. Blue has big dumb stompy creatures and black has small hasty aggressive creatures and Green can get rid of stuff.
And then furthermore you can mix these colours together and get the kind of things as described by GolgariFTW. Or you can mix them together and do things that are nothing like what has been described by GolgariFTW (but his descriptions are great for what the colours do best. Good luck building a graveyard deck in Izzet).
You can do what you want in this game, and that's what makes it so damn good.