I will be trapping in rattlesnake country and bring my coyote dog during warmer scouting months when the critters will be out and about.

Not sure snakes, I've seen plenty of hounds for hogs have protective vest. I would assume if a hog can't get through a snake couldn't. But the ones ive seen only cover chest,belly and neck area, leaves the legs exposed.

Bit in the nose or neck its the swelling that kills them. Get some medicine from your vet before you go. Dog can take snake bite pretty good except for swelling shutting of breath and then often infection after. Get some penicillin too.

If you like your dog, maybe leave it at home?

Your dog will be fine.

Snakes kill bird dogs in TX. I think those hunters can get antivenin to carry

You can get your dog "vaccinated" against snake bites. Not a cure all, but reduces the immediate reaction and gets you time to get to the vet before symptoms get terrible. You can also adversely condition your dog to snakes with an e-collar if you willing to invest the time.