> Represent[ing] an operation to be performed on elements of an object structure. Visitor lets you define a new operation without changing the classes of the elements on which it operates.

And that is exactly what you can do with higher order functions (or maybe procedures, if your visitor involves a side-effect). Instead of passing a "Visitor" object/instance, you pass in a "visitor" function/procedure. It too can achieve the goal of enabling to implement "a new operation" outside of "the class" (or whatever one uses instead of a class). "Operation" probably also being conceptually closer to function than object, since an operation is about "doing something", while an object is not necessarily actively doing something other than live.

By writing a function that accepts a function as an argument, you leave open the possibility for some other part of the code to define that function (a new operation). If you need to add another operation, you just define a new function. That you can pass in as an argument.