I am a no overshoes/plastic bag person.
A pub is a business but it is normally also someone's home so:
Stone or flagged floor in pub = make boots presentable then ask to enter if no sign. A lot of rural pubs in active agricultural areas regard boots as normal attire but it is still polite to ask if you are a stranger.
Carpet on floor - usualy boots off (acid test: would I walk around my own house in them, including upstairs).
My overtrousers have almost full length side zips so I can get them on and off without taking my boots off or getting mud where it is not supposed to be. I did have a set of overtrousers that had top to bottom side zips but you needed a PhD in Origami to get them on in anything but a flat calm.