I need to set a value to an input field that is located (deep) inside an iframe. This input has no id, name or class.
Is this possible?
I can't simply add an id or the like because the code is coming from an outside source:

If there is only one <input> element, you can refer to it by tag name. With jQuery, you would write:
$("iframe#sq-postal-code").contents().find('input')
Note that this may fail with pages coming from outside, due to same origin policy enforced by modern browsers.