Interesting (to me) to note that three out of the four men in the two clearly 19th-century photographs are wearing their trousers tucked into their boots, not over top of their boots.
It makes perfect sense. If you are riding (or walking) through mud or water, that substance is going to go up your leg if your trousers are over your boots.
I imagine working cowboys still wear their jeans that way. Or they do what OCD does...dispense with the jeans altogether.