Yes, Tabo. It is possible that "internal cooldown" or rather "global cooldown" was added onto WF in patch 2.0. - However, it has always been possible to proc WF of an Auto Attack, Stormstrike, HoJ proc, or any other possible proc that would generate an extra attack.
Of course that doesn't go for Windfury Totem, at least not if the shaman already has Windfury Weapon imbued, because those don't stack.
In patch 2.0, for the release of BC, they gave Shamans the possibility to dual-wield. Because it buffed their dps so massively just to be able to DW, they had to nerf the old Windfury used in vanilla a lot. In what way that nerf was specifically, I'm not entirely sure, but they did nerf Windfury for sure with the introduction of dual-wielding.
Here's how Windfury can be in Vanilla:
The normal maximum amount of swings possible (if the planets align), go like this:
Auto Attack: 1+2
Stormstrike: 1+2
HoJ proc: 1+2
Is if all the 3 sources of swings (auto, SS, and HoJ) proc the 2 extra attacks from WF. A total of 9 swings maximum.
HoJ has a very brief internal cooldown because if it didn't, it could proc off itself, indefinitely, if extremely lucky.
The same mechanic goes for the WF proc. WF proc bonus hits themselves cannot proc another WF proc.
The same rule applies to ALL "extra attack" spells/abilities/items in the game, at least as far as I know.
If that rule wasn't there. Then every single extra attack could proc that same extra attack again.
With that in mind, you can simply look at "extra attack" procs as another chance to proc OTHER "extra attack" effects, such as Windfury, HoJ, Sword Spec, Thrashing Blade, etc.
Not the SAME "extra attack".
Edit: Seems at least Sword Specialization's extra attack can proc off itself, as corrected by Askental below. Meaning it's definitely blizzlike that it has no hidden cooldown.