Poland has 23 National Parks, generally walking dogs is strictly controlled, unless otherwise stated in specified areas. Parks are patrolled and the guidelines are strictly enforced. Best to check the regulations for each specific park.
Dogs should be muzzled and on a lead.
Atywni z Psami.pl (Polish) has each park listed .
Psie Chadzanie (Polish) also has great general information, not only for National Parks.
In Ojcow, dogs have to be on the lead at all times. Tatra National Park -Tatrzański Park Narodowy (Zakopane) has a full ban on dog walking except for Chocholowska Valley where you can walk with your dog on a leash.
Keep in mind also, that if you are visiting the ‘Polish Seaside’ where the beach is within a National Park Area, dogs are banned from the beach, again this is strictly enforced.