A light solution of bleach in water, or even vinegar, should do the trick.

It sounds like you may have other issues that are causing the mold, such as air leaks allowing the moisture to condense on the wood.

You may have your home humidity too high - this causes condensation on the windows in cold winter months. Sometimes with some of the below zero temps people have been experiencing, myself included, the condensation forms even if the house humidity is set appropriately. When you see the water condensing, run around with a towel and dry it off. If it is happening all the time, lower the setting on your home humidifier. If it is happening in a basement, get a dehumidifier. If it is in a bathroom, remind family members to run the fan and leave the bathroom door open after they have showered. Sooz001 above has the clean up.