Personally I’ve only ever come across one Dog at a tral center and it didn’t cause any problems, got talking to the owner and he knocks about on here.
But to be honest when people say there’s generally no rules prohibiting walkers/dogs/horses etc from trail centres, there are centers where none of the above are allowed on the trails and vice-a-versa (riders not allowed on bridle/foot paths).
Any well controlled, well behaved dog shouldn’t cause a problem, however there are plenty of badly controlled/badly behaved dogs out there, that would be dangerous in public let alone in a trail center.
The other day I got knocked clean off my feet by a dog in Delamere Forest, I was “Very” restrained when I found the owner, he just didn’t give a monkies and was another 100m up the foot path!!!