It's not as prevalent because most people get vaccinated, which is great. It's a miserable, horrible disease (I still remember my own misery many years ago), and while my scars aren't too bad (not located in super obvious places), I used to be very sensitive about them and I do wish I didn't have them. But I didn't have the choice "back in the day" - I'm so glad those choices are available now.
Both of my stepdaughters had it - one was miserable with hundreds of small lesions and horrible itching (she spent hours in cornstarch baths), and the other had few lesions but they were deep and vicious, very painful when the water from the shower hit them and they did leave her with multiple scars.
Chicken pox is highly contagious in brief exposure - it's transmitted through the air droplets. So if you're in a store and the person in front of you has it (even though the person may not have symptoms), if they sneeze, you could be exposed. That's how it spread through schools. It's not the "prolonged period of contact" - it's the one sneeze, the one moment of sitting next to someone who has it but doesn't yet have symptoms (which can be a period of weeks). That's why it spreads through schools, because kids sit with 1 kid and have lunch with another and stand in the recess line with a 3rd and are on the bus with a 4th. It's not the prolonged contact at all - it's the large number of people one interacts with. So going to parks and stores and playgrounds and church and so on just magnifies the chances.
It's the same with measles - since people stopped vaccinating, it spreads like wildfire - there was a big outbreak in California from Disneyland (which is ilk ethe outdoor parks you mention), and in Massachusetts we had problems last year because an unvaccinated person who contracted measles went into a grocery store and then to a medical center and sat in a waiting room. So these are not "passive" situations at all.
There's also a connection to shingles so read up on that as well.
Here's the info from the CDC website:
http://www.cdc.gov/chickenpox/about/transmission.html
Please discuss this with your pediatrician about when to vaccinate for all diseases, and which vaccines can be scheduled flexibly and which cannot. Be sure your info is correct and not based on scary articles or talk show personalities with no basis in fact. Some pediatricians are open to this discussion, and others will not permit unvaccinated people to be in their practice because every single visit puts infants at risk. So you may have to find a new doctor - the time to do that is NOW. You want to start your search before it's critical. If you choose a pediatrician who does not require vaccinations, find out how they handle waiting rooms - you could go in for a regular well visit or something like possible strep throat (the "usual" childhood issues) and be in a waiting room with someone who is contagious. Find out what protections are in place. If there are none, then always schedule the very first appointment of the day, even if it means you have to wait a while to get one.
In most cases, the anxiety that you and many others have should be much higher for not vaccinating than for vaccinating, unless your child has specific immune system issues. Infants are usually the ones who are not vaccinated, but if you have an older child who is not yet in school, you need to consider what your reasons are for not vaccinating until later, because he/she will remain at risk for longer than if you vaccinated on the regular schedule.
And be sure to let your friends know (neighbors, family, play groups, library story hour) that you are not vaccinating - it's only fair to them to give them that info so they can make their own decisions. It's giving them the same respect you are asking people to give to you.
My son was in the chicken pox trials in RI (about a 45 minute drive from our house in MA) - we found out about it from a friend who is a pediatric specialist at that hospital. We were just thrilled to be a part of it - while data was lacking from the US, there was plenty of solid data from other countries, so that reassured us. That was over 20 years ago and in all that time, there has never been a problem with the varicella vaccine.
I respect your concerns and your anxiety. It's so hard to get a handle on anxiety especially if you have had problems in the past or if you really have magnified risks. There's so much information (and misinformation) out there, and we are all trying to do the best for ourselves and our kids. If you need professional help to deal with anxiety, please reach out and get it - there is plenty of support for you, and there are many techniques for navigating this.
Good luck.