It doesn’t. You’re radiating heat all of the time. Other warm objects radiate it back. An ice cube will not.
While not technically radiation, the movement of heat through air works similarly enough for this purpose. You put your warm hand near a cold countertop, your hand heats the air and the air heats the countertop, causing you to lose heat to the countertop. You “feel its cold” from afar.
It’s not that the cold is radiating negative temperature, rather that there is a isn’t the same amount of incoming positive thermal radiation from that direction. You feel the lack of incoming heat as lower temperature.
Alternatively your hand might be close enough to touch the cold air that’s lost temperature from touching the ice.
So hold your hand out, it feels neither cold or hot. This is because your hand loses energy due to black body radiation, however, the wall on the other side of the room is also warm, so it also loses energy due to black body radiation. That energy leaving your hand goes into the wall, and the energy leaving the wall goes into your hand. Since these are roughly the same temp, you skin maintains a constant temp since it absorbs the same amount of heat as it emits.
If instead of a wall it was a fire, your skin would warm because the fire emits much more energy than your hand emits, so your skin warms up and you feel that.
If instead of a wall it was a giant block of ice, well then your hand would emit energy, but none would come off the block of ice. This causes your skin to cool, and you can feel that.
the way radiation works is that both objects radiate heat to each other. A cold object radiates less heat back than ambient surroundings and you can sometimes sense it. Ancient Persian [ice houses](https://en.wikipedia.org/wiki/Yakhch%C4%81l) took advantage of this, the ice pool was shaded from the sun during the day by a high wall, insulated from conduction and cool still night air limited convection, the dry air also made for some cooling by evaporation, and clear desert skies allowed the large shallow pool to radiate heat into the night sky which, at about -100C, radiated very little energy back. In fact radiative cooling allowed them to create ice even if the air temperature didn’t drop below zero.
You radiate infrared, losing heat in the process.
Objects around you are also radiating infrared.
Normally, those objects are around the same temperature as you, so you are absorbing about as much infrared as you are losing, so you feel neutral temperature.
If something is cold, it’s not giving as much infrared back, so you are experiencing a net loss of infrared in the direction of the cold object. It feels like the object is radiating cold.
The same way that a shadow moves across a wall when you move your hand in front of the lamp, or the same way a vacuum spreads when you open a spaceship door. It isn’t spreading into the spaceship, but rather the air is rushing out to fill the void. Just the same way that heat rushes into a cold object to fill a void of energy.
Or, realistically, the air is just pressure pushing things out and likewise heat moving into a cold area because it now can, which takes cold out of the previous warm area, but that’s less ELI5.
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