Very good attempt at translation.  Hats off to you.

酒灑一地土也醉， 

drunken earth of the spilt wine, Great intepretation without violating the rules. "Drunken earth in spilt wine".

泪流两颊语生悲。 

expressing sorrow tears flow down their cheeks. Tears on my cheeks expressing their sorrow (as opposed to tears of joy)

喜鵲橋頭相會難， 

crossing the bridge of magpies, they meet once every year,  See Melaminefree's comment on 相會難. Your translation as "crossing" is the most accurate one than ours.  橋頭 implies the crossing of one lover (the apparent movement of the star Altair, towards Vega)
相思河畔流水寒。 

absence of love becomes the winter of rivers past.This is speculative.  Here you are not correct. 河畔流水 describes the coldness of the waters of the Milky Way.  The last 2 sentences draw from the Chinese myth.

I am most impressed by your first line.  A whole new angle of looking; very subtle and indirect in the way of the ancients.

What is this "white grass" in the poem?  The first image is of dead grass.  However, that would be yellow.  So it must not correct.  Is it snow covered grass?  Not so because, the poem is describing forboding events before the actual event main occurred.  The winds came first before the snow.  Context must be considered first before any interpretation.  These four lines cannot be lifted out of the context.  There are 14 more lines in the poem.

This poem was composed in 754 AD, for a friend, a departing general to the northern boundaries.  After much research, "white grass" is a name of a certain flora that is from the north west region that is very tough.  However, strong that they are, with sudden wind, they snapped easily.  Snow in August!  Something to be amazed.  To a southerner, all these are rarely seen sights.

You missed a most essential point in traditional Chinese thinking.  The ancients disdain directness in everything.  They love to do thing in a round about way.  Even in poetry, the do not refer things as they really seem.  The best ones are those than can referred obliquely.

Literal version but not word literal

北風捲地白草折, The northern winds sweeping the ground, snapping the white grass.

胡天八月即飛雪. Under the barbarian sky, snow is flying in August.
忽如一夜春風來, Coming suddenly as if the spring wind of the night,

千樹萬樹梨花開. Causing myraids of pear trees bloom.

You are mixing up with translation and interpretive sessions.  Under the name of poetry appreciation or interpretive class,  paraphrasing or even have your own interpretation of someone's work is a wonderful exercise to learn languages etc.  However, translation is a different creature.  It cannot be translated too figuratively or too literally or the wording intent is lost.  Take an example, without context, what does hand-held means?  There is more than one meaning.

We both are talking about different things.  I am talking about translation and you are talking about interpretive intent.

酒灑一地土也醉， 

drunken earth of the spilt wine,

泪流两颊语生悲。 

expressing sorrow tears flow down their cheeks.

喜鵲橋頭相會難， 

crossing the bridge of magpies, they meet once every year,

相思河畔流水寒。 

absence of love becomes the winter of rivers past.