There are no fees to enter Wrangell-St. Elias, but getting to Kennecott requires logistics (eg. variable parking fee at the end of McCarthy Road, $5 shuttle from McCarthy to Kennecott). While the park and roads are open year-round, McCarthy Road is not regularly maintained in the winter and Kennecott Visitor Center is only open from Memorial Day to Labor Day.
As of 2017, the Root Glacier Trail provides easy access to Root Glacier, allowing for glacier exploring, ice climbing and mountaineering options. The trail begins at the end of Kennecott Road and follows an old mine road through the trees. There are a couple of creek crossings that can have very fast moving water flowing downhill, so please exercise caution. The trail forks about a mile and a half in with one leading to the glacier and the other towards Erie Mine. Heading down toward the glacier, you'll cross into glacial moraine terrain to the edge of the glacier.
There are a couple of great camping sites along this trail, which make for great basecamping sites for exploring the area. There are also ranger-led and guide-led tours that start off using this trail.
This trail has an easy / intermediate rating due to its grade and creek crossings.