Obviously cold doesn’t “radiate” like heat does. What exactly is the name of the physical phenomenon you are experiencing.
I don’t know if there is a name other than “an endothermic process” which they are undergoing. 
Convection.
A person won’t radiate cold, but they won’t radiate as much heat as their surroundings, and the absence of radiant energy reduces the amount of infrared radiation you receive, hence the feeling of cold.
If you’re particularly close to them, or if they’re standing over you or something, you may also be feeling cold air falling off them, but for the most part, you’re sensing a non-radiant spot in the same way your eyes can perceive a dark doorway - by contrast to everything else.
Not entirely related comment, but I thought this was interesting enough to mention: Many years ago, I grew my hair very long - not cutting it for more than a year - it became very thick. After this, I got people to sponsor me to shave my head completely bald (proceeds to charity) - in the week or so after having my head shaved, my scalp was especially sensitive to sensations of hot and cold - I could feel (on my head) the radiated body warmth of people standing quite a few yards away - and could sense the momentary ‘cold’ interruption when something blocked it - for example if I was walking down the street and my companion passed the opposite side of a lamp post.
Ah, but cold DOES radiate like heat does. I’m speaking of the thermal infrared, here.
That is, in optics there is a principle that in understanding what is going on, for most circumstances, you can trace rays the way that photons would travel, or you can trace them backwards. It doesn’t matter which way you do it, as long as you understand that you’re going with the photons or against them. For some physical agencies, like say flowing water, you couldn’t do this, but you can treat light this way to understand how it moves about, how it’s perceived, what a lamp will accomplish, how lenses and mirrors work, and so forth. Recall that centuries ago people supposed some kind of sensory rays reached out from the eye to perceive the world around them - if this equivalence principle didn’t work, their explanation would have been obviously wrong sooner than it was.
From this point of view, a cold person radiates cold.
There are no little objects, like photons, flying away from them. Similarly, in understanding electrical current, in most cases you can say the current flows this way or that way, with or against the electrons, and as long as you’re clear which you’re doing the analysis works fine (in most cases - though some things like tubes break this).
For that matter, although electrons and photons are clearly something, they aren’t exactly little objects in the typically understood human sense of it. I think calling an electron or a photon an object involves bigger simplifications and sneakier lies than saying cold can radiate does.
Colder objects can form a heat sink, instead of a heat source. Is that what you mean, Napier?
Santo, colder objects are generally heat sinks, yes, but that wasn’t my point. I’m saying that the radiation process not only works in the harder-to-analyze sense that the cold person radiates less than everything else and others around him radiate their heat to him. It also works in the easier-to-analyze sense that the cold person radiates cold rays that obey the laws of optics (for long wavelengths like ten micrometers). The treatment that says photons are traveling along rays, and the treatment that says “antiphotons” (or whatever you want to call them) are traveling along rays, will both work equally well in many kinds of analysis, including the one the OP is asking about. In the same way, electricity makes sense if you think it’s based on the travels of electrons or “holes”, except in a small number of situations, and this is why Franklin had to guess which pole was “positive” and it was so many years before anybody found reason to say otherwise.
So, did use your newly found powers to become a vengeful vigilante, prowling in the night in search of criminals and damsels in distress?
Not even a Spandex outfit??
I never quite understood how people could believe that – how did they explain the need for light sources to see?
This goes against everything I understand about heat transfer.
Are you saying it’s just a way to visualize the calculations and perform the analysis? Otherwise it seems, to me, that these “antiphotons” would have a real name?
Why not?
I suppose that it is scientifically more accurate to says that the cold object is sucking in all the heat from the nearby surroundings. But is that really any different than radiating cold?
Similarly, I really don’t see why scientists object to the concept of “suction”. They like to refer to it a “negative pressure”, but I really think the only difference is semantic.
Just like a debt is very real. It’s not just negative money.
It’s not semantics, because the thing doing the pushing is air molecules colliding with the surface of their container. They don’t hit the container, grab on to it, and then pull it with them a little bit; that doesn’t even make sense. In the same vein, cold can’t radiate because there’s no energy available for it to do so.
Everything about you radiates heat, at a level depending upon its temperature (technically the 4th power of the temperature and the SB constant). Your skin radiates heat away from you, and the ambient objects about you radiate heat right back. If a large cold object is taking up a noticeable portion of the visual arc to your body, and you aren’t insulated enough, then what you perceive is a lack of heat radiating from that portion of the room. This is somewhat easy to test - get some high-e glass or another highly transmissive clear barrier, and place an ice cube behind it, such that no convection can occur. Move your hand towards it, then away, and note the difference in perceived temperature.