In predicate logic, can the form of a translation of an existentially quantified sentence be used with a universally quantified sentence? 

That's a lot of words for a simple question. 

But here's what I'm wondering. 

Say we have the sentence

"There is at least one brown horse"

With an unrestricted domain of discourse that would translate to

∃x[Bx & Hx]

If we have the sentence
"All horses are brown"

∀x[Hx → Bx]

That translation seems to say 

"(∀x[) What I say next will apply to every instance of the thing I'll talk about"
"The thing I'm talking about (x) is a horse (H)"(Hx). 
"Whenever the thing you're talking about is a horse, it's also the case that (→) the thing you're talking about is a thing that's brown(Bx)" (→ Bx)

That said. 

1. Doesn't '∀x' seem redundant. Doesn't it follow from H → B that all horses are brown?
Like R → W (if you have rain, then you have water). If that weren't the case, you wouldn't be able to write H → B.
2. Even if we wanted to say something about x, whatever it is, couldn't we write:
(x → H) → B
or
(x → H) & (x → B)
3. Couldn't you also write ∀x[Hx → Bx] as ∀x[Hx & Bx]?
4. And isn't ∀x[Hx & Bx] written just the same as ∃x[Bx & Hx], but with a universal quantifier?
5. So why is my text saying I should write ∀x[Hx → Bx]?

Thank you.