I'm a high school teacher and sponsor an outdoor/environmental education club.
Unfortunately, I have found MANY obstacles to getting kids outside. It seems that greed, lawyers, and litigious parents have successfully destroyed the ability of public schools to offer things like this. Great Job Folks!
I entered a never ending world of liability waivers, paperwork, proposing prospective trips 4 weeks in advance to the school board, face questions such as "How can you GUARANTEE nobody will be hurt?", and having to seek medical clearance (and document it all) for students to simply go on a hike. Yes, a doctor's clearance is needed for a student to walk in the woods if the trip is school-affiliated.
A simple one hour hike on easy trail became a nearly month long process to organize.
The flip side: bypass the bureaucracy and just go...and stake your career and everything you own on NOTHING going wrong.
Not to discourage you, but the system I work within has forced us primarily into the classroom. I teach LNT, we study environmental issues, talk about gear and techniques, involve ourselves in direct-action environmental campaigns, etc.
But actually getting out, especially for anything overnight, is EXTREMELY difficult to make happen.
Wherever you end up teaching, I sincerely hope your experiences are different. This is why I believe private organizations are better at this- there is just far too much liability and schools don't want anything to do with it.