Can Horus LV 8 negate/destroy magic cards already on the field like ALO?

No.

You can chain the effect of "Horus the Black Flame Dragon LV8" to the activation of a Continuous Spell Card, Field Spell Card, or Equip Spell Card and negate it. However, if the Continuous, Field, or Equip Spell Card is already active, you cannot later decide to try and negate its effect with "Horus the Black Flame Dragon LV8". You can only negate it when it is originally activated.

from netrep

Unfortunately, no. However, as long as Horus LV8 is on the field, you may choose to negate ANY spell card that is activated when Horus is face-up. However, if ALO was on the field before Horus LV8 was, then ALO stays because Horus was not able to negate it when ALO was played.

However, here's the annoying part:
If your opponent plays a spell card, and you use Horus' effect to negate it then they choose to chain a card that puts monster(s) face-down, then Horus' own effect is negated because Horus LV8 MUST be face-up for its negation effect to work.

Hope that helps a bit.

If youa re talking about chaining a card that puts a monster face-down (E.g. Book of Moon), then Horus Lv8s effect can be activated again in the same chain to negate that. If it is a trap that you are talking about, then of course Horus Lv8 will not be able to do anything against that.

Yes, I meant some kind of miracle trap that would put a monster face-down, then Horus will do nothing because it's not face-up to negate the spell card it originally was going to negate. Am I correct?

If I remember right, "Horus The Black Flame Dragon Lv8" does not have to be face-up on the field for its effect to resolve, which makes the original argument moot.

Yes, despite what the text looks like, it just has to be face up to ACTIVATE its effect, if it already activated, THEN flipped f/d, its effect will still resolve, you just cannot activate it again after it is flipped f/d

You would be foolish to activate a spell before flipping horus face-down so logic dictates that you should do that first with effects like
Tsukuyomi: when this monster is summoned succesfully flip 1 face up monster into face down defense.
Then u can play all the spells u want (crossout=goodbye horus he he)

This has been answered prolly 10 times atleast, a forum search would have saved time and reduced spam.

Everyone here answered the question already