The first site returned -- Aleutian Islands World War II National Historic Area -- seems like one that would have that Activity but it is not in the list:
"activities": [
{
"id": "B33DC9B6-0B7D-4322-BAD7-A13A34C584A3",
"name": "Guided Tours"
},
{
"id": "A0631906-9672-4583-91DE-113B93DB6B6E",
"name": "Self-Guided Tours - Walking"
},
{
"id": "C7D5A145-F8EB-4C37-9E92-2F6C6206B196",
"name": "Self-Guided Tours - Auto"
},
{
"id": "DF4A35E0-7983-4A3E-BC47-F37B872B0F25",
"name": "Junior Ranger Program"
},
{
"id": "0B685688-3405-4E2A-ABBA-E3069492EC50",
"name": "Wildlife Watching"
},
{
"id": "5A2C91D1-50EC-4B24-8BED-A2E11A1892DF",
"name": "Birdwatching"
},
{
"id": "C8F98B28-3C10-41AE-AA99-092B3B398C43",
"name": "Museum Exhibits"
}
],
I've downloaded the entire Parks.json (for testing and research), and a text search of that content finds only 4 sites that have the Activity "Dog Sledding":
"id": "EE1F4878-00FB-4760-A77F-EA76DB8DEFD9",
"fullName": "Bering Land Bridge National Preserve",
"id": "C0BF2A42-E353-4FAE-B4C4-AA0676B58100",
"fullName": "Denali National Park & Preserve",
"id": "11E73438-0CCC-4441-A76A-1995F67F2D89",
"fullName": "Kenai Fjords National Park",
"id": "6F550E4D-AE26-4250-A674-397E2DF88092",
"fullName": "Yukon - Charley Rivers National Preserve",