Earlier quoted context omitted.
Let's say the rogue planet is a massive, super-cold planet. How big and how cold would it have to be to lower the Sun's energy output just enough to trigger a "Snowball Earth" scenario? Assume a direct hit.
I think the only way this works is if the planet doesn't hit the Sun. One could imagine a scenario (but the orbital mechanics don't work out) where a massive rogue planet enters into the solar system and interposes itself between the Earth and Sun, thus shading the Earth and dropping its temperature the required amount. Sort of like a month long solar eclipse or something. But at that mass it's probably pulling Earth…
For our planet's distance from the sun, I have a hard time imagining how anything without self propulsion could maintain a stable orbital position to cast a shade over us for a long enough period (e.g. a month).