Yes! It's very good for your feet to go barefoot, and for your general health as well. Our feet do not 'spread out' from going barefoot any more than our waist 'gets all thick and fat' from not wearing a bodice like the women in the 17th century do... that's their natural shape! Almost all shoes, especially women's shoes, are too narrow and push our toes together. Nor do we need arch support; a survey of people in Asia who had never worn shoes included many rikshaw coolies, who ran barefoot on pavement all day long, and they had *very* few foot problems, far less than Western folks with all their fancy footwear! It's possible you may get flat feet or too-wide feet if you're obese, but that causes problems in legs, knees etc too... if you're normal weight, going barefoot even on hard surfaces is NO problem.
Disease is unlikely, while the dirt on the ground is very visible, our skin is made to keep pathogens out and generally does a very good job of it. Unless you put your feet on the table or lick your toes, you're at little risk. We're at far greater risk of picking something up through our hands; while the dirt on surfaces touched by many people (shopping carts, railings, door knobs, money) may not be as visible, these are covered in as many or more germs as the ground... and with our hands we're much more likely to transfer those germs to our face and/or food, where they *can* enter our body.
The cold doesn't harm us either; if you keep the rest of your body warm, it's possible to go barefoot in cold temperatures without discomfort. I've been barefoot all year round for over ten years; I used to be sickly from early fall until late spring, coughing and sneezing all the time, nothing helped. Since I've been barefoot that's gone. I've called in sick once -for all of two days- and even having a minor cough is rare.
Injury is unlikely as well, feet get very tough very quickly. I never divert my step no matter how much glass I see and I get a tiny splinter maybe once a year, never had a cut. Just in case I do have my tetanus shot, but that vaccine has been around since the 1920's, provides very good protection, and really everyone should keep it up to date; there are other ways of catching tetanus apart from stepping on a rusty nail barefoot.
It's sad there is so much bias against going barefoot in the US, for the fears are unfounded. Fortunately the people in charge of the law know better than the average bloke or store manager; in spite of persistent myths there are NO laws against going barefoot in stores or restaurants, insurance companies don't require or even recommend shoes for customers, and there are NO laws against driving barefoot.