One of the world's largest non-polar ice caps and surrounds are preserved for as long as the ice lasts via the Wrangell-St. Elias National Park, the largest of all U.S. national parks. It encompasses a huge area in southern Alaska, abutting Canada's famed Kluane National Park to the east and home to more than 150 glaciers that make up more than 60% of Alaska's glacial ice.
It's not exactly an easy place to get to, but it sure is worth the effort. The Wrangell-St. Elias range is most easily accessed via private car, though there are other limited options. Check out this Driving Park Roads page from the National Park Service for more information, too.
First, make a stop at the Wrangell-St. Elias Visitor Center in Copper Center and explore the exhibits and bookstore. Stretch your legs on the short hiking trails nearby, and don't hesitate to ask a park ranger to help guide your trip. Check out the Kennecott Copper Mine and drive the McCarthy and Nabesna Roads (beware road conditions). If you can make it out there, don't miss paddling Ice Bay.
Summer is the peak time to visit, and the only viable time for most travelers due to harsh winter conditions. Though the park doesn't technically close, winter snows make travel difficult and dangerous. Find more on planning your visit and hours of operation, here.
Dog lovers, rejoice! Pups are allowed on trails in the Wrangell-St. Elias National Park and in the backcountry. Just be aware that pets may attract unwanted attention from wild animals, especially if running off-leash.