A. Three seems to be the age when many parents begin to wonder whether they should cover up. Unlike the happily oblivious and nonverbal baby, a 3-year-old is a curious creature who will point and prod and verbalize his thoughts about his parents' fascinating bodies (with jiggling parts and body hair!). The scrutiny can be uncomfortable for moms and dads.
Yet it's normal for family members to see each other sans clothes at times (getting out of the shower, getting dressed). And preschoolers are constantly invading their parents' bathroom and bedroom. Your child won't be permanently scarred if he sees you in the nude. Both of our girls, at ages 11 and 8, are still blasé about family nudity, so we still walk from shower to bedroom naked. I trust they'll let us know when it's not okay.
But if you're uncomfortable going au naturel in front of your child, don't start slamming doors and running for cover -- he might start to associate nakedness with shame (think of the therapy bills!), and you'll have to pull double duty demonstrating that you have an open-door policy on questions about the body, appropriate and inappropriate touching, and, in time, sex. Instead, explain that the human body is natural, beautiful, interesting, and nothing to be ashamed of, but Mommy likes to keep her private parts, well, private.
The bottom line: Follow your own lead. If you feel uncomfortable, go ahead and put on your robe.