Being able to work with "Any" implies either working with Strings (since you can encode anything in strings) or it implies a memory unsafe language (e.g. working with void* in C) or it implies subtyping and hence an OOP language.
But OOP subtyping is already about solving polymorphic call sites at runtime. And because you carry a vtable around for every instance, thus objects being tagged with their classes, you can always do upcastings and downcastings. So OOP languages are already very dynamic on that scale and fairly unsafe.
No, you cannot do ": Any" in Haskell.