I just mop with a microfibre pad - I have a few so just attach, spray a bit of dilute floor cleaner on the floor and swoosh around. I have a washable microfibre mat by the patio door which does deal with the worst of it
No, it works great unless there are big clumps of mud - in which case I would wave a broom around, but usually I can corrall any larger bits so I can just use a dustpan and brush at the end. I have this mop, but keep meaning to buy the spray mop - we had one like it before but it broke.
The mat was one from ebay - I searched machine washable rug. It's no thing of beauty, but at times like this when I have three large dogs who are hoolying in and out of the house after doing laps of the garden it is brilliant
Crate next to the front door. I have tried cleaning the paws with a dry or a damp towel, does not do much to golden retriever paws though. I also have an inexpensive "mud mat" from Lidl both in front of the door and inside the crate. For cleaning I tend to wipe up the mud while still wet with a microfibre cloth or mop. Otherwise it just gets smeared everywhere between the dogs, kids and hubby.
Mud mat and an endless supply of doggy towels by each external door. Works better when you haven't got a tall young dog who's taught himself to open doors to let himself and the old rescue in........................