dogs... Ok, cool. and FWIW that dog in the video sure wasn't on any leash...
but I'll bring one. Ours would sit in the truck pretty much the whole time, she's 10 and can't run all day like she used to, I'll get her out if there is some big obstacle where I'm worried she'll fly up and land in the front seat or something, then someone can just hold her for a minute, otherwise she'll be curled up in back. I have wheeled enough to know that the last thing you want is a dog in the way just when you have the line and momentum, and they sure can complicate recovery efforts too.
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