Havok Behaviors is free (http://www.havok.com/try-havok), and we could make new animations with that, the only thing we need is a compiler for Skyrims game-specific animation format (hkp) so we can add new weapons, mounted combat, etc ourselves?

We can, there are tools that decompile the behavior files for Skyrim and can recompile them... The problem is that there is only one behavior file for humanoids, so when you want to modify them you cause conflict with any other mod that edits the same file.

No, I mean define BRAND NEW NON REPLACING animations.

Yeah, like I said... You can... But there is only one file that handles those animations, so essentially every mod with new animations edits the same file, thus conflict occurs.

Well isn't there a way for Bethesda to change that? They seem to be able to define new animations for features rather easily. This is quite crutial for many different kinds of gameplay altering mods.