Originally Posted by BreakableRider
The round pen should not cause any anxiety, if a person is doing something to cause anxiety in their horse about being in the roundpen it's going to show up other places as well.
This. Round pens aren't required to work a horse, many people just find them convenient. I've successfully halter broken untouched 2 year olds and also taken first rides in a large open areas, when that was all I had at my disposal. Good horsemanship creates the good "connection" with a horse, not your desired choice in artificial tools/aids/enclosures.
Any horse I am working is expected to follow my direction, no matter where we are. I'll grant a green horse a few minutes to get used to new surroundings, but I feel getting right to business without babying works better for most horses - whether it's a solidly broke horse, a completely untouched horse, or a previously abused horses. If you confidently proceed, with compassion, the horse will generally follow your lead. If you cautiously tiptoe around, the horse will be nervous, because your body language is telling him the scary boogie man could jump out and get you both at any time.