As long as your skillet is well seasoned, washing it - and drying it immediately - are fine.
From
http://www.geocities.com/NapaValley/4688/cast-iron_skillet.htm"Cast-iron will rust if not maintained properly. By following a few rules, your skillet should remain rust-free and ready for use for a very long time. Here's a few things you can do to keep your cast-iron skillet in tip-top shape:
Cast-iron should never be wet when not in use. NEVER put your cast-iron skillet in the dish washer.
Foods cooked in a cast-iron skillet could contain twice as much iron than they would cooked by other, non-stick skillets.
Rusted cast-iron CAN be saved!!! Scour the pan with steel wool and then scrub the pan with hot, soapy water then scour with steel wool again before drying. Don't forget to reseason as described above!
When finished cooking with pan, scrub the pan under hot water. Place on a warm burner for a few minutes to dry. When drying is done, drizzle some vegetable oil in it. Rub the oil over the inside ok skillet with a paper towel - make that skillet shine! Let skillet cool.
Cast-iron corrodes when acidic foods are added. If the skillet is well-seasoned, corrosion is not likely. Be sure to remove acidic foods from the skillet immediately when cooking is finished."
I've got some cast-iron skillets and pots, as well as a huge bean pot, that are more than 25 years old. I've always "washed" them.