Precisely . :yes:No you shouldn't have to on previously painted wood, Wren, as long as you've sanded it down evenly.
This is a really good idea. They definitely should be cleaned and cleaned squeaky clean. Vinegar is perfect for this if you decide not to sand.I have a cousin who always wipes down trim work with plain vinegar before repainting. He says it gets any film or grime off and dulls it a bit so the new paint will stick better.