"In the winter, there are no flowers blooming."
Why does winter take the は particle and no the に particle?
The use of に or は here is not substituting each other.
Time words may be used by itself or followed by the に particle.
Usually time words using like an adverb are not followed by に, such as 朝, 夜, 毎日, etc.;
Time words using like a noun must be followed by に, such as ３時に, 1月２０日に, 誕生日に, etc.
Seasons like 春, 夏, 秋, 冬 are in middle of the road, they can be followed or not followed by に, and the preference depends on the context.
Example: the Wiki for Sakura says Sakura is a plant that
The sentence in concern is negative and there is no actual action in the sentence (vs. saying Sakura, a particular type of flower, blossoms at a particular time, the spring, in the Wiki). は is used only because 冬 is being brought up as the topic, and about this topic, a fact is observed (no flowers are blooming).
It is possible to use に and は together though:
In winter, I want to go to hot spring.
The whole sentence is bad. It shouldn't be present progressive either.
In certain syntax they are interchangeable, but we need more details to know whether you and I are talking about the same thing.
Firstly, we have to clarify about the difference in the concept of "Bloom" and "咲く”
"Bloom" in English means the process of flower buds growing from the branches until the flower is open; However, "咲く” is the process that the flower petals stretch until the flower is wilt.
In spite of such difference, in a negative sentence as in here, "flowers are not blooming" and "花が咲いていません" do not have material difference in meaning. Both of such negative sentences are just describing that the event to have flower opening does not exist.
In a positive structure, the difference would be a bit more prominent. 咲いている／咲いています would be the state that flowers are open; In English they are "bloomed" but not "blooming".
Thus your sentence さいている花がありません actually means "There are no bloomed flowers". So the listener may have the speculation that you are saying there are flower buds but they are not bloomed. After all, it is not wrong at all grammatically, and the meaning is not completely unacceptable either. It is just a little strange.
It would be viable to say
to mean "no flower (by type) is blooming in winter."
(Lit. There is no flower (that) is blooming in winter.)