Nah, Haskell has no functions with zero arguments.
You could say that a value is a function that takes no arguments, but then you lose the distinction between functions and other values, and more importantly, the distinction between function types and other types! For example, types like Bool have decidable equality, but function types in general have undecidable equality, so you really don't want to be caught saying that Bool is a function type. It's much more sensible to say a type is a function type iff it was constructed by the type constructor ->, which takes two types, the argument type and the return type. In other words, all functions take one argument and return one result.
You could also say that a value is an unevaluated thunk that takes no arguments, but that's not always true. The thunk may be already evaluated and replaced with a value, without affecting the visible type. It's better to keep the idea of "thunk" separate from the idea of "function", because a value could be both, either, or none.
You could also say that every value x can be converted to and from a function () -> x. But that's not a function with no arguments, that's a function with one argument of type "unit" (the type with a single member, a.k.a. the empty tuple).
The above might sound pedantic, but for some reason it's fascinating to me to think about such things. Language design is a kind of addiction and Haskell is like a drug, because its original purpose was to be a laboratory for programming language research, which you can see in the million GHC extensions.