I live on a world where most places on my planet has four seasons, just like yours does. We also have one sun and one moon, presumably. It's been not even a year since I came of age (20), and we've gone through the four seasons about a dozen times. I repeat, it has not yet been a year.
The people on my planet are very similar to humans on your world, and a side-by-side comparison would show this. Our animals are much like yours also, with minor exceptions that aren't really relevant. The only difference between us and your people is that we're much more resilient to the elements, blunt force trauma, and so forth. Several times each, I've survived electrocution, being blasted in the face by fire, and falling off a tall building where I fell at least 5 stories, probably more (usually being caught by something before hitting the ground, but not in a way that would make the impact much safer) and suffered minor injuries at most from each of these. So if the reason means the conditions of our world are somewhat less hospitable compared to yours, that should still be fine, as long as our world isn't a hellscape. (Our world is actually quite pretty with rainforests, cities, crystal clear oceans, fields, and so forth.)
That said, we have holidays like you do. We have Christmas every winter (not once a year, but every winter,) and Halloween every autumn. Our birthdays, however, are only once a year, just as yours are.
I've always found this strange, though. With one sun and moon, it makes little sense that we'd have the four seasons multiple times. From my understanding, the four seasons should still only happen once... right? Is there an explanation for how this could occur naturally? If not, what about unnaturally? Could this be caused by a specific tilt to the axis?
EDIT: Some supplementary information. We are a globe planet, technically an oblate spheroid, like Earth. Not a flat world like Discworld, nor are we other abnormal shapes. Also, I'd like the answer to make sense through science, without the need of "magic" as an answer.
Additionally, we define our seasons astronomically, I presume, but I'm no scientist. I just know how the patterns change and how we celebrate holidays. We don't consider just any moment we get snow to be winter, but there are periods of the year where snow is much more likely which we refer to as "winter", but that isn't to say snow in the other seasons is impossible, just less likely.