Ocracoke requires no permit and as far as I know, except when there's a whole lot of rain, most ramps should be open - especially the airport ramp and the road that goes to the southern end (right across from Howard's Pub). Just stay out of the dunes, nesting areas, and turtle hatching zones. It's cool to drive around the southern point to the backside of the island around Teach's Hole. This is where blackbeard was killed. Bring a tow rope if you have low ground clearance, there are plenty of people that will offer a tow.
As far as low/hi range, I have driven an automatic 2.8 wagoneer (a real p.o.s.) with no issue in 4 hi, and an automatic AMC Eagle (with no low-range) with no issue on ocracoke beaches. Have seen subarus out there and 2wd suvs, though unless you are really experienced driving on beaches, and the sand is packed, 2wd is a bad idea. My Eagle was loaded up with people and dragging the diff. the whole way, but it cruised right along and got some serious head turning. That was fun...
My opinion: a stock 4wd explorer will be fine in 4 hi without lowering the tire pressure much (say to 25 psi) if you drive confidently and smoothly. If you are dragging in the ruts, get out of them and find some shallower ones. Go with your gut. If it feels like the truck is working really hard in 4 hi, stop when you find some harder sand and switch to 4 lo. The whole reason I am so stuck on 4 hi, is that I don't want to spend 30 bucks in gas for a day on the beach.