Yes as far as I know
Dogs are allowed on all of the South Rim trails. Dogs are not allowed inside buildings (unless service dogs) and are not allowed below the rim. There is also a kennel on the south Rim for those owners that want to hike below the rim. Have fun! My 3 dogs loved the rim trail!
No problem. Just keep him close. That is a large place with lots of places to get lost in.
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