How is the horizon problem really a problem? I always thought the uniformity in the temperature of the CMB was supposed to be expected, since it's a much more probable initial condition for the universe. I finally found someone explaining what I mean in much better words (link):

Horizon problem isn't really a problem
If we examine from statistical mechanics principles what thermal equilibrium really means, we see that it is the most probable macrostate for a system (in other words, the state with highest entropy). Systems evolve towards thermal equilibrium not because nature has any sort of preference for evening out energy among all degrees of freedom, but simply because having a roughly equal partition of energy among degrees of freedom is OVERWHELMINGLY probable.
For exactly the same reason why it is overwhelmingly probable for a closed system to move toward thermal equilibrium, it is overwhelmingly probable for a completely randomly selected initial condition to be in thermal equilibrium. No causal contact is necessary.

The only "counter-argument" I could find for that, ironically enough, comes from Jason Lisle (link):

(...) in the early universe, the temperature of the CMB would have been very different at different places in space due to the random nature of the initial conditions.

But if that "random nature of the initial conditions" is of the same order of magnitude as quantum fluctuations, wouldn't that apply to the early instants of inflation too? If so, how would thermal equilibrium be even possible under such quantum fluctuations during inflation?
 A: I’m not sure I fully understand the question but I’ll try. The “curious one” says that if the initial condition is picked at random then it should be a state of thermal equilibrium (maximum entropy) since the overwhelming majority of states look equilibrium-like. Now there has to be something wrong with that in the cosmological context. States of thermal equilibrium are static and the world is manifestly not static.
What statistical mechanics actually says is that for a fixed total energy most states look like thermal equilibrium at a temperature that depends on the total energy. In other words, for a given energy most states maximize the entropy. If we don’t constrain the energy then the state of maximum entropy has infinite energy and is not really a state.
Even more to the point, the idea of energy is very confusing in general relativity. In a cosmological setting the total energy is always zero. So the whole framework of statistical mechanics and maximum-entropy states is not well defined. To put it bluntly there is no theory of the initial state. That’s the problem.
What inflation does is it makes the later history very insensitive to the initial state. Whatever theory for the initial state is put on the table, inflation will wipe out its memory. The result of inflation is a “fixed point”  or “attractor” which means a particular behavior that a very wide class of initial conditions will result in.
Leonard Susskind
A: The problem stemmed from having to deal with how such a vast region of space had such a fine tuned uniformity. Without inflation that same volume could not have maintained the same uniformity once you consider the mean free path between the particles. Thermal equilibrium requires not only a high temperature. It also requires a sufficient density to allow the reverse reactions to occur.
Prior to inflation the temperature and density is sufficient. Then inflation occurs. That sudden volume change would normally cause a sudden cooling. If inflation has multiple waves or perturbations there would have been anistropies crop up. However the slow roll process at the end of inflation caused a significant reheating effectively wiping slate clean of any previous anistropies and previous particles that were not in equilibrium. This makes determing which inflation out of the 70+ inflation models more difficult.
The latest Planck dataset favors an inflation model with a single scalar and low kinetic term. However this does not rule out multiscalar models.
http://arxiv.org/pdf/hep-th/0503203.pdf"Particle Physics and Inflationary Cosmology" by Andrei Linde 
http://www.wiese.itp.unibe.ch/lectures/universe.pdf:"Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis 
These articles will help the finer details see chapter 3 of the second one.
http://arxiv.org/abs/1303.3787
