When we first adopted Mingus we lived smack dab in the middle of Portland, Oregon. We had a 1/2 acre and were able to set up our corral to conform to city code, so we even had a permit for him.
We had a city park (Mt. Tabor...an extinct volcano) three blocks from our back gate, so we frequently walked him on the park's roads, bike paths and hiking trails. Even the grass was mini-friendly, since the park also contained the city's water reservoirs, so no chemicals or pesticides were used in the park.
Wanting him to be a good citizen, I called the Parks & Recreation Dept. and asked if this would be okay. The head of security told me that horses are welcome in all of Portland's parks, and that our mini was probably less of a nuisance than some of the dogs -- all he asked was that we carry a big bag and dispose of any unsavory items.
The only real problem was that a planned one hour walk lasted two or three hours, due to all the attention.
When we added Thelonius, things became even more fun, especially the time a GSD fell in love with our new boy, grovelling at his feet and pledging his undying devotion! We took them along on a picnic with the neighbors, with Mingus carrying two market bags slung over his back as a make-shift pack. Even the saké made it without a problem.
We now live out in the boonies, where we frequently hike on logging roads. We don't go too far off the main roads, as there are bear and cougar in the area.
We have a Rails-to-Trails path about two minutes from our house, designed for horses, bicyclists and hikers, so we haul down there and drive the path. We carry a longe whip along with the driving whip just in case we run into unfriendly dogs. Mingus loves dogs and always wants to sniff any that come along. So far, all have been leasheed. The bicyclists we've come across are incredibly considerate, pulling over to let us pass.
We did come across riders, but we all saw each other and we stopped while they passed us. Good thing, because one of the big horses was indeed terrified.
We also have a state park nearby that has many acres of riding paths. We horse-camped, hiked and drove with Mingus, which was a blast. The park ranger were uncertain about the cart on their trails, but they were assuaged by the pneumatic tires (rightly or wrongly) and by Mingus' charm. Every big horse person we met asked about him, driving, and minis in general, saying they wanted one for themselves.
We learned that, when horse camping, you should be prepared with a mini-safe gate. This camp has big horse sized chain gates, and there was no way that was keeping even a 38-inch mini inside. Fortunately, we had a sheet of plywood that makes the floor of the horse box in our cargo van, and it fit the gate per. We bungeed it in place and it worked perfectly.
Then there are those Oregon and Washington beaches that allow horses...so fun it shouldn't be legal! We had our first beachdrivers' weekend before Mingus was trained to drive, so I led and ground-drove him while others drove.
My suggestion would be to always ask permission. You may well be pleasantly surprised. Portland is definitely progressive in this regard (they're even talking about allowing minis on the city buses and light rail trains!?!), but don't assume one way or another.
Mingus driving on the beach.