Dogs
Two off-leash parks in the county, and a straight answer per state park — including the one that bars dogs all summer and the two that allow them everywhere except the bit you came for.
Town of Oakland
Oakland Dog Park
27 Oakland Rosedale Road, Oakland, MD 21550
A fenced off-leash dog park on the town walking trail, free to use. The town's own words are "a clean, safe environment" for "well-behaved canine citizens" and not much else — most of what's known about the inside of it comes from a magazine rather than from the town.
Free
Deep Creek Lions Club
Garrett County Dog Park
1249 Bumble Bee Road, Accident, MD 21520
The county's other off-leash park, inside the Lions Club's McHenry Community Park — which is the reason to pick this one over Oakland's: restrooms, pavilions, a trail system and a disc golf course are all a short walk away.
Cost not confirmed
Nine of the twelve state parks have no published pet rule I can find, so this page says so rather than assuming leashed-and-fine. Neither dog park publishes its hours, and only one of them publishes a price. If you've stood in either of them, that's the fastest way to fix this page.