Big Bear has a very casual vibe, and even in the nicest restaurants, jeans are the norm. Locals tend to wear flannel shirts and jeans, often forgoing warmer jackets. Many surf/skate/snow brands are also worn as part of the outdoor culture. Visitors wear just about anything they like but keep in mind a few tips. I am writing assuming you are coming from Southern California and are used to a warm, mild climate.
In the summer, Big Bear can get hotter than you might expect a mountain town to be. Bring tank tops, Shorts, and sandals that you can get wet in your chosen water activity. The nights sometimes get chilly, though, so pack a light jacket and pants in case the weather dips.
Autumn in Big Bear is so lovely and often brisk. While October can be warm during the day, it isn’t unheard of to get snow in November. Make sure you pack warm socks, gloves, hat, and jacket.
Chances are you expect it to be cold in the winter and will pack jackets, gloves, beanies, and mittens. Long underwear can be nice to have under clothes at night as well as warm socks and insulated boots. Winter boots also look nice and could prevent you from slipping on icy sidewalks.