I read somewhere that in Spain the people dress according to the season and not so much according to the actual temperature. Is this true?

If it is, what season will they be dressing for toward the end of October? I'd like to make some effort to not stick out like a sore thumb - if that's possible.

In late October, dress like you would in New York city at the same time: lightweight wool, nice clothes (casual but nice); women tend to wear pant suits or short skirts and blazers; men wear nice shirts and pants w/ a sweater or jacket. Leather stuff is big. Light dressboots. The big no-no's are always: athletic shoes; team sport/athletic clothes; t-shirts; warm-up suits/jogging clothes. If you are a jean person, a neat outfit based on jeans is appropriate for walking around. I always feel more comfortable in black jeans than blue! rgf

I think you´re right, Madrileños dress acording to the season and not actual temperature (but it´s not general), it´s curious to see in September, with the first real Autumn days, people dressing Summer clothes with 14º, this is normal because in Spain most people aren´t interested in the weather and they dress like the last days, and Madrid has radical temperature changes, one day you can have 28º and only one day later you get only 14º.