I have to confess that, for all the Westerns I've seen, the question of "How did saloons lock up for the night when they just had those swinging doors in front?" never occurred to me.
Short answer: most saloons in the Old West didn't actually have those silly little doors, and those that did just had larger doors that could be closed in front of them to lock up at night (or address the cold of winter).
And now you know.
How Did Saloons in the Old West Lock Their Doors at Night?
What stopped no-good varmints from crawling underneath the doors?
I too, have stayed up all night pondering the same question.