Could an icy/extremely-cold asteroid/comet ever strike and cool the Earth? This is obviously an imaginary question, but it seems like something computable (which I don't have the mathematical ability to do so unfortunately). P.S. I do not have in-depth knowledge about comet/asteroid/meteoroid/even any space object at all, so please correct me if I made any mistakes. Also, please answer the question considering the current state of the Earth, not a super-heated Earth.
Some propositions:

The asteroid/comet is sizable, cold to the core, and is made up of materials with high heat capacity
The asteroid/comet &quot;strikes&quot; the Earth at low speed
The asteroid/comet strikes the Ocean

Related: How gently could a comet/asteroid/meteorite “hit” Earth?
Could an icy/extremely-cold asteroid/comet ever strike and cool the Earth?

No.
The smallest possible velocity is about 11 km/s velocity, and that would require a near miracle. For that to happen, the object would have to enter the vicinity of the Earth through a very small keyhole near the Sun-Earth L1 or L2 point with a very small velocity (a comet will not have that very small velocity), then be nearly ballistically captured by the Moon, and then fall to Earth. A comet would be more likely to hit the Earth at 40 km/s, or larger.
And that means that it does not matter how cold or how hot the object was prior to impact. The kinetic energy of the impact will dwarf whatever thermal energy the object had prior to the impact.