DOG FRIENDLY: No, Getting to Funnel Arch does require one small section of a scramble (class 2), so I advise not bringing dogs or kids.
PERMIT: No
FEE: No
VEHICLE REQUIREMENTS: 2WD
TRAILHEAD COORDINATES: 38.519494, -109.602566 (Google Maps will shown an official TH but find this starting point easier)
I'm not going to recreate the wheel here -- this is the best blog I've seen on this hike: Hiking to Funnel Arch, Moab – Girl on a Hike -- this hike does involve Class 2 scrambling with exposure. Please read the attached blog for visuals and I've attached my photo of me scrambling the crux.
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I have created curated maps and itineraries for travellers that want to travel like me.