It seems like 雨 or 雪 are viewed as weather phenomena, which are more black-and-white (either it rains/snows or it doesn't) whereas wind lies on a continuous spectrum. So to say "windy weather" (which in English also should be understood as "stronger than usual wind") in Japanese it seems more common to say 風が強い, meaning that often during the day the wind tends to be towards the "strong" end of the spectrum.
In English, "rainy" or "snowy" can be understood as "raining/snowing on and off", (similarly "gusty"). On the other hand, you can't say "haily", presumably because "hailing on and off" is not perceived as a natural weather condition.