You could blame the laws of thermodynamics and say that cooling is much harder in our universe because of them. However, since we're in a dark energy-dominated universe that's expanding and cooling, it seems as though cooling is generally easier for the universe on the largest scales.
Even on smaller scales, cooling is usually easier (I've of course determined ease by observing which one happens more often). The cores of planets will cool and harden over time, stars use up their fuel and cool as they die. Cooling by far is the easier process. Even when the universe reaches a heat death (assuming it ever does), the expansion will continue to cool it to lower temperatures. So cooling is definitely easier for the universe.
So why isn't cooling easier for us? Well the answer could be due to thermodynamics. It could be that on short time and distance scales, it is easier to heat than to cool, but let me present a more anthropological reason.
Throughout human history, we have always strove to perform tasks. We want to build buildings, grow crops, light our homes. All these tasks require us to expend or use energy. As such, we have invented brilliant systems and processes of generating easy-to-use energy and channeling it where we need it to be. We have become very adept at taking energy from a few common sources and dumping it into wherever or whatever we want. And, as we all know, putting energy into an object is much the same as increasing its temperature. So, for us, increasing the temperature of something is no problem. It's generally what we do. However, to decrease the temperature of an object, you need to remove energy from it. Now with the exception of those few specific sources, we aren't very adept at taking energy out of something. That has never really been as necessary in history because usually when you remove energy, it makes it harder to do any tasks. What would the point be of making it harder to perform tasks? As such, we rely mostly on natural processes to remove the energy from systems. But unlike the processes we invented, natural processes usually try to bring temperatures to thermal equilibrium. Sure, we invented refrigeration and we found a few endothermic reactions to exploit. But when it comes down to it, we're much more interested in putting energy into things (computers, lights, heating systems, anything requiring electricity) than taking it out.
It could simply be the case that while the universe finds cooling to be easier, we have put a lot more effort into figuring out how to heat things and so that is easier for us.