Yeah, usually—but not always. In most cities, public trash bins do come with lids, and a lot of modern ones are designed to stay shut in the wind. The ones that work best tend to have weighted flaps, spring hinges, magnetic latches, or a self-closing design. Those features stop the lid from flapping open every time a gust comes through.
That said, you’ll still see bins with lids that blow open. Lightweight plastic lids, loose hinges, damaged latches, and overfilled bins are common culprits. Some cities also choose open-top or semi-open bins because they’re easier for people to use quickly, but those are more likely to let litter escape on a windy day.
So if you’re asking because you’re choosing bins for a windy area, I’d look for self-closing or weighted lids and check that the latch or hinge feels sturdy. A good lid should stay closed in normal wind, but still be easy enough for people to open with one hand.