Anyway, I think I understand why we use 'on' in this case. When we say summer nights, sunny afternoons, windy nights, etc we have to use 'on.' I need think them as days. Am I right?
Basically, yes.
On the night I was born? Why 'on'? :-(
Despite what some members seem to think, there's
almost always a 'logical' reason to choose one preposition over another. The trick is to understand the basic meaning that each preposition expresses. This meaning comes from the way the mind of the speaker views the
spatial relationship expressed by the thought.
When using prepositions of time such as
in and
on, we still have
spatial structures in mind. That means that we view time as if it were space, where bits of time are seen as things like objects, frames, points, etc.
In the case in question, you're right to say that
on winter evenings is a bit like saying
on Tuesdays because the mind is thinking about the prepositional object in a similar way—in this case winter evenings are seen as a 'block' of time, (on which an action or event can be placed) rather than as a 'sweep' of time (in which an action or event can be framed). Very basically and simply speaking, we use
on for blocks of time and
in for sweeps of time.
Another useful point to make here is that when a speaker wants to specify a time phrase,
on is the preferred preposition.
In the evening, I was playing video games.
On Tuesday evening, I was playing video games.
In the latter sentence, the evening is
specified in some way. This is also the case with your example of winter evenings. A good explanation for the difference here is that the specification creates sufficient distance of viewpoint that a sweep of time resembles a block.