Do you own a trench coat? If so, how/when do you wear?

I feel very drawn to them! Especially the ones below. However, they're not popular where I live and so I feel a little confused about how/when to wear and what they're for. My climate: toggles between snowy and hot and is on the arid side. (We don't get a lot of rain and it can seem like it's either summer or winter with very short spring and fall).

To my eye, they skew a little dressy. People dress very casually where I live and outdoor wear tends to be gear. People dress in layers. I'm worried, because of the length, that a trench would be either too warm or not insulating enough for my climate.

Is a trench coat meant to be a rain coat? So confused.

Show me your favorite trench coat and tell me how you wear!