Also I would probably eliminate the comma before "golden red hair." That's a unit, so you don't need a comma before it. But that's not a big deal.
Her breath kept fogging up the window, and she had to keep wiping it clear with her fingertips so she could see the black and gold gilded state carriage, drawn by six fine bay mares bearing thick brown manes, as it rumbled through the Gate House and into the courtyard.
The sentence is too long, probably. I'm not sure where to break it, but notice that you have "as" there, which makes it seem like the carriage is only drawn by bay mares with brown manes at the moment it rumbles through the gate. First off, the main action of the sentence probably shouldn't be relegated to a subordinate clause. And also, it's just too much going on for one sentence. Let's see-- well, I'm not sure how to get that action into the main clause.
Her breath kept fogging up the window, so she wiped it clear with her fingertips. Then she could see the black and gold gilded state carriage, drawn by six fine bay mares bearing thick brown manes, rumbling through the Gate House and into the courtyard.
or (this is formalish syntax, so it can probably handle a bit of inversion):
Her breath kept fogging up the window, so she wiped it clear with her fingertips. Then she could see, rumbling through the Gate House and into the courtyard, the black and gold gilded state carriage, drawn by six fine bay mares bearing thick brown manes.
"Bearing" is a bit clumsy-- they don't CARRY their manes, do they? With thick brown manes, maybe?
I think the next line or sentence should be something important, something that gives us more info about her or why the carriage is important or something. The description is good and vivid-- but it's time for something to happen now. :)
Alicia
This is something different to my first offering ... only two sentences, albeit long. BTW, the explanations you have posted already are really useful - looking forward to seeing a few more!
The young woman stood alone at the window casement; her deep green cloak wrapped over her shoulders and pulled tight, the hood hiding her long and wavy, extraordinary, golden red hair.