Yes, October is still the rainy season in Haikou and Sanya. The average temperature is about 23~28C, it is hot and humid. Anyway, it is hard to predit the weather at that time. You'd better pay attention to the weather forecast during that time.

I just returned from Hainan Is. It was much warmer than Singapore. The heat is unbearable esp in the village where the old houses are built close together. In Haikou you can escape the heat by staying in the shopping malls and restaurants. There are McDonalds & KFC restaurants also. Food and transport are very cheap compared to Singapore. Bus fares within the city is only 1 Yuan (S20cents). Don't visit Hainan Is from May to Sept if you prefer cooler climate. October should be Ok. It get colder in Jan. Try the high-speed train from Haikou to Sanya, travelling at 250KPH for S$23 first class.