This will not work at all
The short version
If you drop an ice cube into a room temperature drink, the drink will be slightly colder for a little while. But what happens then? Answer: the drink warms up again until it has the same temperature as its surroundings.
What happens when these melt? Does the drink stay cold? No, it does not. (Image source)
The long version
The issue with global warming is not that we are accumulating heat in such a way that if we can just manage to make a one-time dump/soak of heat, then we will be all right. It is not as if we are sitting on a warm rock that must just be cooled off a bit and then things are fine.
Four things to keep in mind for further discussion:
- If you gain more heat than you lose, the temperaure rises. If you lose more heat than you gain, the temperature drops. If you gain as much heat as you lose, the temperature remains constant.
- The surface where we live gain heat from the Sun and from the inside of the Earth
- The surface where we live lose heat by radiating it into space
- The rate at which we lose heat is proportional to the fourth power of the temperature of the surface
The heat that we gain is more or less constant, save for geographically local variations. This does not vary to any great degree. The amount of incoming heat is for all intents and purposes the same over the time-spans that we care about.
That we lose heat proportional to the fourth power of the temperature means that the temperature on the surface of the Earth will be very stable. Because if the surface cools, it radiates a lot less heat, and this is then balanced by the incoming heat, and will warm up the surface again. Conversely if the surface warm up it will quickly radiate a lot more heat. The incoming heat will not be enough to compensate for that which is radiated out, so the surface cools. So this is a sort of self-regulating mechanism.
The factor that messes it up for us is the atmosphere. The atmosphere is like a big blanket for the Earth. Some of the heat that is radiated away from the surface does not disappear into space but is instead reflected back to the surface again, the so called "greenhouse effect". This means an increase of the incoming heat.
Now if this reflection is constant, or changes only very slowly, the balance between incoming and outgoing remains constant and the temperature does not change very fast. We can adapt to any slow change. This is the way it has been throughout most of civilized history.
But if the greenhouse effect becomes more pronounced, and this happens fairly quickly, then more heat is being reflected back to the surface, and this upsets the balance. It is like swapping a thin blanket for a thicker one. Now we have more incoming heat than before, and this is not balanced by the outgoing heat. This means that the surface will warm up; its temperature will rise until there is balance between incoming and outgoing again.
Dumping some ice onto the planet will not help. While it is true that this will soak up some heat it is a very transient effect and will only cool the surface for a short while. The cooling caused by the ice soaking up heat upsets the balance between incoming and outgoing. Now there is a big difference between them, because the now cooler surface radiates a lot less heat. So the laws of thermodynamics will quickly restore the balance.
There is only one way that we can stop global warming and that is to make sure that more heat is dumped into space again. This we would do by thinning out the "blanket" that is greenhouse gasses (GHG), chiefly carbondioxide but also methane and some other GHG. We would thin it out by halting the emissions of these gasses into the atmosphere, and then let natural processes take their course, by which already existing such gasses are either broken down or integrated into sold matter, such as plant life.
Some suggest we can prevent also some heat from reaching us, with so so called Climate Engineering, but those plans are... eh... "unsure cards" to put it mildly
