As said by @dwohnitmok it depends on the domain you consider. If you have a proposition quantifying over objects and functions operating on said objects, it's second order. But if you have a proposition considering only said functions as objects, it is first order (with a different domain: not the base objects, but functions over those objects).
And again: you can ignore such subtleties for most of mathematics.
And again: you can ignore such subtleties for most of mathematics.