@Joshua's answer is correct and addresses "cold wall of incubator". I want to add on the more general question
I don't get it, can you radiate "cold"? If someone can explain how a cold wall/cold bottle/ cold anything would affect the baby by radiation (and not by convection).
Everything reaches a radiation balance given time, the radiation leaving a body and the radiation impinging from the surroundings ( including air) reach a balance and the temperatures equalize, environment and body.
When there is generation of heat in a body, as with a baby, the temperature is higher and is sustained higher than the environment. A baby in a crib with enough covers adjusts its temperature easily through biological mechanisms. A premature baby has not yet well developed all these mechanisms of response to environment. An incubator creates an environment to buffer the changes happening in a crib in an open air, and keeps the loss of energy from the baby at a comfortable and safe range.
Convection in liquids and air happens when there are differences in temperature within the mass. Convection transfers mass at a given temperature, and thus the black body radiation balance between the room and the incubator can change, the incubator radiating from the walls more energy than it would if the air were warmer. This is the way cooling by fans work , in a computer for example. A fan brings in cooler air for the radiation balance and takes away the heated air that would keep the temperature of the mother board higher .
Thus convection works with changes in the boundary conditions in the given situation, changing the temperature of the environment in which the body is embedded. Within an incubator though, there is not enough mass of air to create convective currents of any strength unless the temperature difference baby/wall is enormous, and even then it is the radiative loss that is dominant.
Does placing a cold bottle next to an incubator cool the incubator through convection or radiation?
A cold bottle next to an incubator will also change the boundary conditions for the radiative situation, and the walls of the incubator will cool radiativeley faster because of this. There might be a small convective effect but the masses of air involved are not enough for convection to be important.
Now the feeling as if ice radiates cold is just that, a feeling of the faster energy loss of a hand close to ice.