Eye of Skadi as replacement for Heart of Tarrasque on meele carries?

We have different definitions of carries.

Though admittedly necrolyte, Leshrac, and Krob (pushing/tank/teamfight) could be considered a subtype of carry at this point.

Well, Queen of Pain would actually be a viable hero to get Eye of Skadi, but there are more important items for her like Linken's Sphere. :\

It's by no means a bad item, but if you want a slow, the [Orb of Venom] is a much cheaper way of getting the job done...

Another thing: I normally get Sange and Yasha on skeleton king. I really like every stat it gives me, like MS to catch up, a slow, attack speed, HP, damage. I normally combine it with Armlet of Mordiggian, Assault Cuirass, Heart of Tarrasque, Power Treads/ Phase Boots and a Divine Rapier(can be replaced with other items, for exaple Black King Bar, but skeleton king uses Divine Rapier best from all heroes). I also really like Ring of Aquila for earlygame, way more than Magic Wand.

What do you think about that?

That is viable :)

Eye of the Skadi, even though seems to look good on paper is not really a favorable item for melees, most that is as there are only a few Melee Carries that can easily close the gap between them and their target. The first hero that would come to mind when thinking about melees viable for EotS would be Spectre since his Haunt illusions spawn close to enemy heroes and automatically target on them giving him full use of the Movement Speed debuff.

Do I need a slow?
Do I need mana?
Do I need armor/attack-speed?
Do I need tankability?

These are the questions you should ask yourself when you are thinking about puchasing it, since it does not give a significant amount of DPS.

So unless the carry you are playing does have a significant way to make use of the slow and stats or already have a great overall DPS, it is generally not worth it or a Ultra late-game item.
Illusion-melee carries make great use of it, especially PL.
And I think Lifestealer also deserves a special mention, since HoT sacrifices too much DPS for tankability (since he damages mostly through Attack-speed due to his Feast ability) and you will not hit enough times in the short duration of his slow, then I think a Skadi is a great alternative to keep him buff and on the same time eat frozen tanks, it will also solve his mana-problems too.
But there are a lot of melee carries already mentioned so I will not bother with those.

Edit: Oh, and: Am I an illusion based hero? Should also be a question to consider XD

I'm pretty sure Skadi's effect does not apply when an illusion attacks. It used to with Orb of Venom, but they patched that.

I was referring to stats, since Eye of Skadi offers a variety of them. So while the original PL slows the chosen target more and more "buff" illusion will appear, and that enemy will have no escape.

It's good on characters that gain greatly reduced benefit from items that only add direct damage. No matter what your primary stat is, you get +25 damage from this, and some characters make more use of stats than others.

On one character in particular, this item actually gives +125 damage.