One of our founding Fathers (or mothers in this case) by the name of Tillie Simion once said, "Red River is Great For Men and Dogs But Hell On Women And Horses". The hell that the women and horses faced back in the day has definitely subsided but the fact that it is a great place for Dogs still holds true.
The cool weather combined with the endless forests to roam and explore make for a dog paradise. Go for a hike through the woods, take a swim in the river or just lay in the grass and nap in the morning sun your dog will most likely not want to leave.
As far as accommodations, you will find plenty of properties that will cater to your furry friend. A quick Google search should bring you plenty of options to choose from.
But whatever you do, don't leave your dog at home as he will enjoy Red River as much or more than the rest of the family.