While I have a huge industrial cutting table at work, if I sew at the cabin, I cut on the floor in the living room/kitchen or in the dog trot. I often sew in both places, too with a treadle. That is based on season: hot in the dog trot/wrap porch or cold in the kitchen. Or I'll take my hand crank to the patio in the trees, but a digression (and why yes, I DO use a sad iron there).
Cutting...I use cutting mats. The Dritz Foldable Superboard Cutting Surface...I have two of them and use pound store table cloths under the whole area. Largely because I have a working farm at the cabin...a dog, a donkey, a mule, a goat (with a kid any day), several cats, chickens, a pet rooster (not mine...DDs, but the thing will come sit on the chair in the dog trot with her) and god knows what we all walk through between the animals, the hay, the mud, the woods, the air and the fact I am outside more than not.
TL;DR: floors are easier with a cardboard cutting mat.