I came to this site because I was trying to figure out the meaning of "the fiery and snuffy are raring to go." After looking over the various posts and thinking about what seems logical to me, this is the conclusion I reached.

An old Paint refers to a pinto type horse, and an old Dan could be a dun but is definitely a pack horse or mule, since it is being led. The hoolihan or hoolian is a rope throw since going to Montana to rope wild horses certainly makes sense in context of a cowboy's life. "They" then refers to the wild horses. The dogies are being enjoined to ride around the wild horses slow so as not to spook them when they are being rounded up, because they are "fiery and snuffy" and liable to stampede (only one contributor I saw came up with this as a solution or indeed said anything at all about what this meant - sounds good to me).