Yeah, the costume change is a bit of a stretch. There's like 2 panels over the course of which he takes his outer layers off, revealing the costume beneath. The way I envisioned it, his costume "booties" are more like combat boots anyway, so they work as his civvy boots. So basically he just keeps the costume under the jeans and jacket.
Frankly, everyone would rather draw Wolverine in costume than out, as much as it makes more story sense. This is for fun.
And yes, it is all set at night.