How hard does an air conditioner work if the outside air is cooler than the inside air?

An AC is a heat pump.   It pump heat from INSIDE the house to OUTSIDE the house.  

You will be losing heat from INSIDE the house thru the walls and windows so most likely the temperature inside will be going down naturally.   Once it goes below 70 the AC will not kick on and your house will continue to cool naturally.  It will cool down to roughly the same as the outside temperature.     If you want to maintain your temperature at 70 you are going to have to turn on your furnace.   

How hard an AC works is set by the heat load in the area being cooled. That is the number of BTUs that have to be removed. The lower the outside temperature the less energy is required for the compressor to do its job. So depending on how you want to define "hard work" the answer is different.

until your cooking heats the room above 70, it doesn't work at all.  Then, it will require only minimal work.  Probably, you'll want to use the heat strips inside the air handler in order to keep the temperature above 60 anyway

at that temperature you could damage the unit if it doesn't have a low ambient kit on it.⁰⁰

It would be easier to cool the room, but gosh if it is 50 outside, why would you not just open a window

It is colder outside.  You need a heat pump or a furnace to bring room temp to 70. 

If you use the AC and set it to 70 and the room temp is higher than 70, it will work for a few minutes and then stop when the room reaches 70 and will not turn on again as the room just gets colder and colder.  If the room temp is very much lower than 70, it will not even turn on. 

On newer units with a temp sensor in the condenser, the unit will not turn on if the outside temperature is lower than a set temperature, normally 65 deg F.