When you think about it, it makes sense for the seasons to change every month instead of every 3 months--it won't be Winter everywhere at the same time, for example, so at least this way, one month out of three corresponds with each real-world season for everybody. And this way, we also don't have to wait as long to reach a certain season so we can access a specific location (Winter) or battle a specific trainer (Spring).
Anyway, I love the seasons addition, and my favorite season is Winter. Still, the seasons are a bit disappointing in some regards. The only differences between the seasons, excluding the aesthetics, is the aforementioned trainer battle with Cynthia, minor things like Castelia Ice being open or not, and different Pokemon in the wild--and the latter still only applies to Winter. There could definitely be more changes within each season.
Also, I'm disappointed that only a few cities have snow in Winter, and only one of them is ever truly blanketed in snow. How awesome would it have been to see Castelia covered with snow? :(