For the column to permanently remain cold it would have to break the laws of thermodynamics.
I think it all depends on the how the column works but I can think of two possible outcomes.
The column is magically isolated
If the column never absorbs heat then it would remain cold.
That would also mean the surrounding environment would never dissipate heat to it and therefore would remain entirely unaffected.
The column is a void for heat
The column does in fact absorb heat, however all the heat is absorbs is magically destroyed.
If this were the case then it would absorb all the heat in the immediate area until it reached -100 also.
It would then presumably stop when the heat transfer rate of the air around the column was the same as the heat transfer rate of the sun over and around the area.
For the heat transfer rate of the column I need to take a couple of assumptions.
First I'm gonna assume the column is placed on the ground not into the ground - I know this is unrealistic but it makes it simpler.
The next assumption is a big one - size. 400ft (121.92m) tall and lets make it relatively thin with just a meter radius (3.28ft), also assuming its a perfect cylinder.
So given that the average temperature (obviously very variant) is 31 ºC or 304.15K that gives us a temperature difference of 104.15 K.
In addition the thermal transfer will be different in the ground and air.
There is lots of different thermal ratings dependant on soil.
Choosing a clay based soil the thermal coefficient is 1.1 W/mK.
For air this is 0.0262 W/mK
Plugging these into the equation Q/t = kAdT that gives us an initial transfer rate of approximately 360 W through the ground and 2.1 kW in the air.
Therefore total energy to counter balance this would be 2.46 kW
If the column is destroying heat the temperature difference will remain constant and therefore so will transfer rate.
Finally the sun gives us 1 kW/m^2 of thermal energy on the ground (assuming the surface is perpendicular the entire time).
This means the area would reach only 2.46 m^2 around the column, though this is a bit of a mean estimate. This area would 1.34m radius from the centre of the column or 0.34m around it.
Edit - The Day & Night Cycle
So I know it's been a few days but I've been thinking on it some more and realised I missed one pretty huge factor... the night.
For a quick recalculation the moon reflects 12% of the light of the sun.
I know this is subject to the moons phases but as with the rest of the question I'm taking large assumptions and averages.
The next of said assumptions is that the moon reflects light in the same proportions as the suns light (UV, visible, Infrared) and therefore its energy transfer is also proportional at 12% of 1kW/m^2 (120 W/m^2)
If this is correct then the 2.46kW transfer rate will need a much larger area to be countered.
This area would be 20.5m^2 around the column, 2.74m radius from centre or 1.74m out from the pole.
Obviously this would be hugely varying dependant on the cycle of the moon.
On a new moon night the area would reach as far as possible in the 12h (again avg) of no sunlight it has, with this being limited by the transfer rate.
On the flip side this area would be almost half the size on a almost full moon night, but not half on actual full moon as on a full moon the light of the sun is blocked by the earth and therefore wouldn't reach the same amount of light reflected back on the earth.
The cold area would fight a constant war between day and night expanding and shrinking.
This massive heating and cooling effect would have similar properties to large desert areas and over time I think the dry area would create a desert like effect around the cold zone.
You could include some species that would take advantage of this cycle and move into the area in the day for some of the nutrients or plants it creates.
Certain desert creatures and plants may like the area but would have to be introduced mostly.
However the area size wouldn't make much wiggle room.
If you were to also state your pillar is very thick then the area around it would increase in a square proportion to the radius of it, giving you a larger varying climate to go with it!
Edit if you can...
If you think my calculations are wrong or I missed something then suggest an edit.
I will double check it against sources to confirm it, if you name the source all the better.
However I know I've probably made a mistake or overlooked something so please do suggest!
The area outside of the absolute cold area would be very dry as water may be frozen out the air.
It'd gain moisture for a while then lose it again as it became water vapour.
I doubt it'd be enough to form a lake but in the middle of the cool zone you'd get a lot of snow/sleet/rain.
Also can recalculate if you give more values.