Absolutely, cats, dogs, birds, several breeds of exotics. Just nothing that can be officially considered "livestock". A micro pig is cool, but A 300lb hog is not.
Yes
They certainly are. When our grandson died, I went to Texas to be with my daughter and we stayed there. We offered to pay a deposit, but they said they didn't require it. That the pets were welcome. My daughter brought her dogs to the hotel every night that I was there and they spent the night with us. It was a very friendly atmosphere.
Yes they are.
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