Yes they allow well behaved dogs on leashes. Please clean up after yourself!
I would check with the management, there may be some requirements, considering that, with that many plants around, a dog may consider even the covered areas to be an outdoor environment. Also, given the limited space inside the covered nursery area, I would not recommend taking larger dogs there.
Yes, many people walk their dogs around Flowerworld. You might want to be careful around the lake area, because of the ducks, etc., but the nursery section is fine on a leash.
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