I wear jeans, converse and this coat in winter. But on sunny days with no chance of getting wet I also wear a boucle jacket, a blazer or a wool peacoat.
There's a mixture of stuff on our school run. Most are casual in jeans or there's gym/running gear or work outfits. Dd now in y3 and I haven't encountered any bitchiness or stares yet as everyone's lovely.
Unless I'm in gym gear I accessorise with lipstick. As a sahm if we don't dress up for the school run, when can we?