I know that for prayer (davening), you're supposed to be dressed "appropriately", e.g. not in your pajamas; the rule of thumb I'd heard was "as you normally would when seen in public." (Rabbi Enkin has a post about the "hat and jacket" on Hirhurim.)
What if I'm fully dressed, but I also have on top of that my -- winter coat? Gloves? Ski mask? How important is it that I take those OFF before davening?
I'm assuming being over-formally-dressed -- e.g. tuxedo or coat-and-tails -- is never a problem? (Unless you can't concentrate on your davening because everyone in shul is making faces at you ...)