Frozen blossom

[flotsson]

Jack

You have bested me again
Winter                 this is obviously personal taste, but I find using both Jack and winter to be needlessly repetitive; I would recommend you either insert Jack instead or remove Jack altogether. 
With your clever endeavour                 the internal rhyme here feels tonally off. A bit too playful and bouncy. 
grasping on with your frost-bitten hands                  visceral and evocative
Awaken sun and spite the cold          it's at this point that I feel a little lost. Who are we talking to? Jack, who already won? If it's more of general wish or command, or to another personage altogether, I would consider indicating that in the text with a line break, or ideally a few extra lines/reordering.
Warm the day and colourise the flowers                 I like this line a lot, but I would consider a different verb than colourize, it's a little too direct and a little too awkward.
Make them beautiful, bright and bold                 once again, great line, no notes. 
Run through the trees
Awaken the flora                 you already described this and the repetition adds nothing to my eyes; I would consider removing the line or move it to the start of the description if you're set on the repetition
Ring spring, throughout the land
Tell Winter their work is done                this is a bit pedantic, but invoking Jack Frost implies that winter's work should be "his work". Normally not a thing I would bring up, but it adds to the general ambiguity surrounding to and about whom we are addressing these lines.
Now begone
The world is in my command
To those who seek me, I will come
Find me in the morning dew                 
With blooming buds and vibrant hues, 
I'll paint the world anew                  in my opinion this would be a really strong ending if you added a break here. As is it's a bit unwieldy, but it works. This is entirely personal. You can even keep the rhyme, if not the internal rhyme, by changing "hues" to hue if you're married to the rhyme here

Hi, I liked this poem quite a bit. The only more general note I would give is to consider the use of more punctuation. The poem works fine as it, but I personally find a poem much more readable at this length with a little more guidance.