I grew up road riding. There literally were no horse trails in my area (Hialeah--outskirts of Miami, Fl). If you didn't want to spend your life on the farm where you boarded, you got out there and rode, regardless of the terrain. I went over interstates and under them. Down the verge of four lane roads, through neighborhoods (sometimes showed up at my own house for carrots and water), galloped across my high school field, got burgers at the drive-thru, swam in rock quarries. So the idea of hacking out just doesn't give me willies. It's what you do.
That said, I always spend time with an unfamiliar horse in a ring. I won't ride it out into the world until I understand how it responds to cues under controlled circumstances at all speeds. I also want to know how it moves, where its muscles take me, what its gaits are like--all so I understand what it might feel like if it spooked. Once I know all those things, I start trail riding.
There are ladies at the barn where I lease that NEVER ride outside of an arena. They literally tack up at the barn, and then LEAD their horses several hundred feet across the property to the indoor arena, where they close the door behind them before they mount to ride. They do not ride one step outside of the indoor arena. If they are leading a horse back and a car comes along, everyone gets real nervous.
Other ladies there do ride outside of the arena, but are horrified when life comes at them on horseback. They don't want their horses scared or distracted at all.
Their horses are all beautiful, well-cared for animals. Their owners ride frequently and get great pleasure from it. I can't really fault them, even if I would get bored senseless riding in the arena every day.
So you? Ride as you like. Where you like. Your horse will adapt, unless it gets ring sour, which isn't usually going to happen if you aren't pushing it constantly with no relief. Ride in the arena until you are comfortable on your horse, then slowly begin hacking out. Ride as far as you are comfortable, then turn for home. Next time, ride a little further. There are many adventures to be had on the trails. It's good for the mind or both human and horse, and it will make you a more competent rider in the end.