Hi Eldar,
Yes, you seem to have to have your dogs on a leash almost eveywhere here in Arizona. Also, many parks (the National parks) don't allow dogs on the trails even when on a leash. That makes it more difficult for traveling with dogs. By the way, my collies are very well trained and would not really need to be on a leash as they are gentle and very well-behaved, but we just follow whatever rules there are when we are hiking on trails.
bev