No they are not, from what I've seen, your restricted to the alliance. So as an imperial you have 4 styles to choose from. I crafted the goofiest set of bosmer heavy armor today.

Actually!

When you start a new character, that character can only craft in the style of their race. Since you have an Imperial, that means that Imperial is the only style you can craft.

However, as you explore you'll find books called Motifs. Each Motif is tied to a race (for instance, there's a Breton Motif and a Khajiit Motif and, presumably, even a Daedric Motif). If you find and read one of these Motifs, you'll unlock that crafting style for your character.

And no, you are not limited to the styles of your alliance. Any character can craft any style as long as they've read the Motif book for that style.


[Edit]

Is that even what you're asking, though? You're not talking about the race, but the color schemes. I believe that the color schemes change with the quality/level of the gear you're wearing. I suspect you'll find the gold color scheme you're looking for at higher levels.

The gold coloured armour is made from Dwemer ingots (I think) These are high level crafting materials, like 36+ I think. The black coloured armour is made from ebony (I think), an even higher level crafting material, like 46+ (I don't know the exact levels tho) You are not restricted by your class, alliance or race. you can wear every armour piece, as long as you are high enough level.

Oh and you can only craft other racial armour styles if you find the correct motifs to craft that style.