Emphasis mine.
To me, this is an oxymoron. Suburban is suburban. Rural is rural. You can no more have a rural suburban field than you can have an urban country market.
If the situation is as described in the OP, that is, truly a rural setting, then I would agree with the older gentleman. Picking up after your dog in such a setting, IMHO, makes you look rather pretentious. Do you think anyone picks up after the horses, cattle, goats, chickens, etc… ? The likelihood of anyone else running across the dog’s leavings is pretty slim and, if they did, they would just view it as being as natural as a half-rotten stick of a dead bird.
If it is actually a suburban setting, even one with an occasional horse field, then the population density is much higher and picking up after a dog would probably be viewed as being environmentally conscious. Where I lived in Texas, I was definitely outside the city and my neighbors had chickens and horses, but if I was walking my dog and he crapped, I’d pick it up. I didn’t pick it up in my own yard (nearly an acre), or if he went in a vacant lot, but in someone’s yard, you bet.
In a city, with sidewalks and curbs, I would not have a favorable impression of someone who did not pick up after their dog. The population density is just too high.
Funny thing, in France, picking up after your dog seems to be unheard of. I spent quite a bit of time in France a few years ago and dogs are everywhere. In restaurants, bars, tied up to poles outside grocery stores. And, they poop on the sidewalks and medians. People just walk right past it. Maybe not in Paris, but in the smaller towns in the north it was pretty common; so common that there were workers who sprayed down the sidewalks and gutters, washing the shit into the drains every day. I doubt you’d find a Frenchman picking up after a dog.