Let me offer a different persepective on this. Cooling is not universally harder than heating. To demonstrate this, consider the following:
Suppose you have two 1 kg copper blocks, one at 200 K, and one at 400 K. Put them into direct contact, and seal them in a perfectly-insulated (no heat transfer from the walls) empty box. The 400 K block will then cool to 300 K just as readily as the 200 K block warms to 300 K. [N.B.: The 300 K final temperature is based on the simplifying assumption that the heat capacity of copper is temperature-independent between 200 K and 400 K.]
But, you might protest, aren't there many instances in which cooling is more difficult—e.g., cooling vs. heating a home? The answer is yes. But then what distinguishes the example I've offered from those that concern you? The difference is that you are specifically referring to cases in which potential energy (PE) (typically electrical energy) is used for heating or cooling.
Given this, I would suggest your question be refined as follows:
Why is it harder to use PE to cool than to heat? Now I can give you an answer:
PE can be converted to thermal energy with no losses, thus achieving heating directly with 100% efficiency. E.g., I can convert electrical energy entirely to thermal energy using a resistor. [This ignores losses in getting the PE into your system, e.g., resistive losses in electrical transmission.]
However, PE cannot be directly converted into the removal of thermal energy. Instead, to use PE to cool requires running some form of heat engine. And, by the 2nd law of thermodynamics, even a perfect heat engine cannot be 100% efficient. Furthermore, all real-world heat engines operate dissipatively, and thus will be even less efficient than a perfect heat engine.
So, in summary, if you are talking about the conversion of PE to heating vs. cooling, the difference is that the former can be done directly, with 100% efficiency, while the latter always requires going through some form of heat engine, with significant attendant losses (as well as [with some exceptions, such as a Coolgardie safe] significantly greater engineering complexity).