Of course, we can't be sure what Walt would do or say, but he did have an incredible eye for detail and passion for the purity of the experience he wanted to create for people ... human people!
He wanted to create a place and experience that takes us humans away from our everyday stresses and he worked on this considering every angle and last detail. ...Building sight lines, landscaping, music, no smoking or alcohol etc. etc. etc.. He didn't want anything to break the spell.
Especially if he was alive now in 2017 (bearing in mind his revolutionary, refined and exacting approach), I really do think he would recognise that dogs (beloved as they may have been to him) do not add to the escape and magic he imagined. I think he'd see that not only do dogs actually create stress for groups of people, they also create stress for the environment he was building.
I can imagine him opting for a completely separate resort, with completely separate transport. I can imagine him considering every aspect of this issue and how every eventuality would be managed. I can imagine him disliking the fact that people who loved his fantasy world are falling out of love with it because of this development (and others) that jolt one out of the magical environment he held dear.
Everything Walt Disney created that was new, fantastical and cutting edge didn't come about because he followed the crowd - the crowd in this case being other hotels, resorts, places for human leisure.