Learn Farsi: در زمستان برف می‌آید.

In Farsi, there isn't a single verb that means "to snow." Instead, you say that snow "comes." The noun برف (snow) is the subject, and می‌آید (it comes) is the verb. So literally, this sentence means "In winter, snow comes."

Is this how you talk about all weather in Farsi?

Yes, this is a very common pattern! For example, to say "it is raining," you would say باران می‌آید (rain comes). For weather events that fall from the sky, using the noun plus the verb آمدن (to come) is the standard way to express it.

Why is the verb in the present tense (می‌آید) if this is a general fact and not necessarily happening right now?

The prefix می is used for both ongoing actions (it is snowing right now) and habitual actions or general facts. Since "it snows in winter" is a general truth, this present habitual form is exactly what you need here.

In spoken Farsi, would people actually say در زمستان?

They might, but in casual, everyday speech, Iranians often replace the formal preposition در (in) with تو or توی. The words themselves also often get shortened in pronunciation. So in a conversational setting, you are very likely to hear تو زمستون برف میاد.