"I do not wash my clothes in fall and winter."
I assume you think は is a subject marker?
は is just a particle that marks context, it can sometimes marks what you are calling a subject but is not always the case. When you see 〇〇は、this is not important for the meaning, the thing marked by は is only there to let the listener know what we are talking about it, most of the time this is omitted because is understood by context. 〇〇は is important for context. は can sometimes marks the
So you could say in this regards that the sentence has 2 parts「秋と冬は」「服を洗いません」"speaking of fall and winter, I don't wash clothes (around that time of the year)", where the first half of the sentence is there just for context and has less importance to the meaning, while the second part is the meat of what the speaker is trying to say.
You could use に as well to mark 秋と冬に、this marks the time as more specific and most probably will change the meaning of the sentence from a habit you are describing (not washing clothes in those seasons) to a decision like "I will not wash my clothes in fall and winter", but since we are only just describing what we do in those seasons and not other ones, the は particle does the perfect job.
You could also phrase it with は marking the "doer" of the sentence (sometimes called "subject" in English resources) like「私は秋と冬に服を洗いません」But I'm pretty sure this sounds less natural, you don't always need to include 私 in a sentence, is understood if the words are coming out of your mouth already.
If you wanted to be more specific while sounding natural you could also use が which is the "doer/be-er" marking particle, this is the equivalent to the subject in english, but since this is not expected, it creates a strong emphasis that is "you" who does this action.「秋と冬は私が服を洗いません」"it is me who doesn't wash clothes in fall and winter".