Dogs are a bit of a "use common sense issue" but here is information regarding the area from the 3 different landowners involved.
From the Lower Seymour Conservation Area website.
"Dogs must be in control at all times and leashed in high use areas and in sensitive ecosystems. Show courtesy to other visitors by removing your dog waste and disposing of it in dog waste bins located at main entrances. Dogs are not permitted on the Seymour Valley Trailway, the Fisherman's Trail (north of the Homestead Trail junction) and the Rice Lake Loop Trail. The LSCR does not permit commercial dog walking."
You would have to define high use area and sensitive eco-systems. If there are no signs to designate that area as such then it would be up to the conservation officer (and the dog owners common sense). My dog is off lease all the time up there but I leash her when we are near places like Salmon habitats but I also like to believe that I exude common sense.
From BC Parks website regarding Mount Seymour. (I don't know anyone that follows this and I don't know anyone who has gotten in trouble from a BC Parks officer for it.)
"Pets/domestic animals must be on a leash at all times and are not allowed in park buildings. Signs are posted and fines are issued for pets off their leash. You are responsible for their behaviour and must dispose of their excrement. Backcountry areas are not suitable for dogs or other pets due to wildlife issues and the potential for problems with bears."
From the CMHC website regarding dogs on Mount Seymour.