Good job!

Here I go, with nit-picky-ness. If you're super-sensitive in regard to your writing, do not read this. It's decently close to critique 'stead of sugary compliments. If you do read it, I hope it helps. :)

In the spring,

Birds sing, bees fly, and all comes alive.

Flowers bloom, sweet scent fills the air. I think that if you had more in-depth, descriptive phrases, this passage would be infinitely more effective. As it is, it only feels cliche.

Leaves bud and fill, turning darker. A better line

The world is filled with color,

The sky is blue, the water is clear, "The sky is blue" needs a simile, a metaphore, or at least a good deal more description. Same for the rest of the line, actually.

The flowers dot the world like a million drops

From an artist's rainbow paintbrush. I kind of like this. Nicely done.

The sun is pale yellow, the clouds are floaty white, the nights are black and cool and dark and full of life. About now I'm thoroughly tired of your repetative structure. Try varying the last few lines a little so that they're not all "The _____ is ______."

The mountains

Tall and shadowy

The guardians of the woods Good line, I think.

Are shedding their snowy white tops

For darker colors. Describing those other colors would help here.

The poem is a little long. I would put a stanza break here and between the other seasons, although they sometimes merge together, so that could be difficult. Just a thought.

Summer brings its hot fiery sun, 

Orange now, floating in the sky. You used "floaty" just a few lines back. This feels repetative, and not so much in a good way.

Animals are growing, the world has gone lazy. This line kind of contradicts itself. "Animals are growing" connotes movement, action, a swelling frenzy of the world. Then you say that everything's lazy. I would drop the first part of the line, as it seems to fit better in the spring stanza. It is also lacking in description - if you include it in another part, I would spend a little more time on it.

Rain falls and brings relief, the creeks and streams turn to rivers.

The world has darkened, and is less bright. One of the fundamental rules of writing that I think you need to work on in this whole poem is "Show, don't tell." You're a little too fond of being verbs, not using enough action.

The mountains rise over all,

Tall shadows, purple, black, blue,

Keeping watch on a droswy world.

Autumn's first frosty breath is the breath of life,

It brings movement.

Suddenly all is run-around hurry-scurry,  I like these dashed phrases. A good feeling of that frantic rush.

Preparing for the long white cold ahead. I would change the middle of this phrase to "the long cold white." Can't really say why except that it seems a little too normal right now, if you know what I mean.

The leaves begin their change of wardrobe,

Slipping into cloaks of red, yellow, gold, orange,

Fiery, they make the world

An eternal sunrise and sunset.

Frost forms in the morning,

Pale, clear, glistening. This season was distinctly better than the rest of the poem so far. Much nicer. Good description, good action. That's what you need in the other parts.

Leaves begin to float and fall,

Their bright colors fading to brown.

In the distance,

The mountains that watched through the summer

Have formed white tops on their peaks.

Winter is coming.

Run-around hurry-scurry and then...

Silence. Mm. I like.

The first snowflakes drift down.

The last traces of the last autumn sunset have faded away.

The snow is small at first, Another place where you need to vary your sentence construction to avoid monotony.

The younglings,

The floating, twisting, dancing little ones

That just couldn't wait

And had to come down before everyone else. I like your idea here. I would not use the word "just" in the line above. It doesn't feel right. Perhaps change that line to say something about their impatience. A bit of rewording would fix it, I think, but as I'm unable to define what's wrong, I really can't expect you to take that advice. :P

But it grows thick

And soft

And silent.

The world awakens late to a white morning.

The trees are bare. *singing* Vary construction. . . .

Firs and pines have heavy, thick boughs

That bend and shake with every passing breeze. This seems like a bit of conflict here. If their boughs are so thick and heavy, why do they shake with every breeze? 

Frost is a thing of the past.

The snow is here. I like these lines, although I think they would be better if a colon or semicolon instead of a period merged them.

The mountains are no longer pure shadow. Look at this poem and see how many lines look alike at the beginning. Again, it's "The ______ is ______." It gets choppy and boring pretty quickly, but it's also a problem that can be fixed quickly and easily, without any change to the essence of the poem.

Their tops are coated in cotton. That is a bit of cliche.

The air is cold.

Winter is a drowsy time, as is summer.

Sleeping is the only thing to do. I like these two lines.

The world has prepared.

Now there is only one thing to do.

Wait for spring. These lines need a colon, not a period.

Here are my overall thoughts. You need fewer short delcarative sentences, more description. The whole poem is a little cliche, but seeing as how I've written a couple that are worse, I shouldn't complain about that. Your fall stanza was good, winter was all right, but spring and summer need rather more work. Decently nice, as a whole. I'd like to see it if you change anything. 

Cheers and so on,

lavendershy

Awesome!