I spent a great deal of my time in Korea walking from one place to another and I often had chance to talk with people. These are just my observations, which admittedly might be skewed due to the fact that I am a foreigner and what Koreans use as small talk between each other might not be the same things they say to foreigners like myself as small talk. Koreans on the site may have better/different input than me. The state of "being a 외국인" and things contingent to such was usually half of the small talk I engaged in.
As you mention, the weather is a commonly used topic for small talk. Korea seems to be no different in my experience.
요즘은 습기가 너무 많아요. It sure has been humid lately.
날시가 진짜 쌀쌀하네요! The weather sure is nippy!
Some Koreans like to talk (both domestic and foreign) politics, at least to foreigners. If I had ₩1000 for every time I have had someone ask me about Barrack Obama, I would be a millionaire. Maybe even in American Dollars.
I also was in Korea during a presidential election (이명박). We talked a lot on the street with people about 정동영, 이명박, and 이회창. (These are the three candidates I remember; there were like 10 of them).
After the passing of 노무현, I had a lot of people engage in small talk with me about his death.
Have you eaten yet?
A rather common phrase I heard/was asked on the street was "(아직) 식사했어요?" (Have you eaten?) They don't actually care if you have eaten. This threw me for a loop for a while, until I figured out what they actually meant. It is just a greeting, almost like the phrase "How's it going?" in English. People do not actually want to hear "how it's going."
Some Koreans liked to ask me if I had tried ________ food (fill in the blank with whatever you want), but I think this was just because I was a foreigner.
However, if you want to start a small talk conversation with a Korean, I found food to be a go to move. This is especially effective if you ask about a regional food. For example, when I was in 춘천, I asked about 닭갈비
예: "제일 맛이 있는 닭갈비집이 어디 있어요?"
Where is the tastiest chicken ribs restaurant? (My opinion: 청산 닭갈비).
Or if I was in 신당동 in Seoul, I would ask about 떡볶이.
One other thing that I heard discussed as small talk was health.
건강하세요? (lit.) Are you healthy?
I think this phrase is very much like "식사했어요?" They do not actually care about your health per se; it is just a way of starting small talk. Elderly people seemed to gravitate to this phrase.