Dog ( Pet ) access is heavily restricted.

To clarify the rules, the main entrance, meaning via Sunken Meadow Parkway is 100% no pets.
If you have to pass the toll gate, whether they are collecting tolls or not ( seasonal ) then you are now entering the area in which dogs are not allowed YEAR ROUND.

The area which allows dogs is accessed off Old Dock Road, the nearest cross street is upper dock road. It appears to be side of street parking as the parking lot on that road down by the water is run by and restricted to Town of Smithtown residents with a valid decal.
This parking lot would be seasonal as well. However even if you access Sunken Meadow park via the beach access there, Pets are not allowed.
Only the trail which starts at the south end of the street parking is allowed to have pets, and only while on leash.

Too many people take their dogs into the park, which is clearly marked in many places as no pets year round, and then let them go off leash and run through the protected wetlands.
While many times this goes without incident, there are areas in which owners have allowed their dogs to be off leash and they chased various wildlife, and at least one person has been given a summons, in this case for "disturbing a federally protect species" which was a piping plover nesting area.
That alone can carry up to a $10,000 fine.
If the dog happens to actually kill one, the fines go up to $50,000.
Is it likely to happen? Not if you keep the dog leashed... but remember fighting any ticket or summons you may get in a marked area, that on it's website states pets are not allowed, will be difficult.

Again... if you are entering the park anywhere other than from Old Dock Road via the back trails ( and restricting yourself only to those trails and no developed portion or beach area ) you are not in compliance.

The area is great... and the trails are nice, a good distance, easy to walk, but are heavily wooded and plenty of ticks... but for a bring fido rating? I'd say no higher than 2 bones, because the vast majority of the park is off limits and you can potentially be fined.

I'm going to upload an aerial image showing in yellow where the parking and trailhead is and the allowed area, along with the off limits area in red.
Hopefully it will be available in images on this site.

Apr. 16, 2022