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.
If it hits the Sun, it really doesn't matter how cold or how massive it is (up until it becomes a brown dwarf at which point we're talking binary star interaction levels of mass).
The thing is that the Sun is really spectacularly huge. You could fit over a million earth size planets inside of it. And it is a run away fusion reactor so it is kind of like throwing frozen beer cans into a 500 acre California wildfire. Very little effect on the fire (although any embedded Hot Shot firefighters will appreciate your effort).
But things are even easier than actually hitting the Sun in this case. If you're trying to just screw up the Earth, any rogue planet that flew through the Solar system and pulled earth more than about 6 - 8% off its existing orbit should completely wreck the climate. If you were a fiction writer you'd want it to be bad enough that people could survive long enough to write a story about it or course.
Generally though any astronomical mass that would nominally qualify as a planet flying within a million miles of the Earth is going to likely trigger an extinction level event. Especially if it is off the ecliptic by some amount.
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).
So yeah, you can't really add cold stuff to starts to extinguish them - stars are made from absolute ice to being with.