Is there an obligation to wear socks while wearing sandals, or is this a Midat Chassidut? Is there a difference between Tefilot to the rest of the day?

The Poskim wrote that we should dress to Tefilot, or even just for entering a shul, in a way customary for dressing in front of important people. Since today most people wear sandals during the summer, even in presence of important people, it seems to me one may daven in sandals even without socks, and of course one may do so during the rest of the day as well. Rabbi Ro'i Margalit