October is something of a transitional month in Singapore with the approach of the Northwest monsoon, which brings an increase in rainfall, usually in the form of late afternoon showers.
October sees a good chance of some rain in Singapore, but still lower than in the November to March period.
October in Singapore sees temperatures averaging around 30 degrees. Bear in mind the high humidity in Singapore, which can make temperatures seem higher.
Much of Singapore is ruthlessly air-conditioned, so consider this if shopping along Orchard Road.