I've taken firey to refer to the hot coals of the branding fire and snuffy to refer to the branding iron used on those coals. ie. the branding iron creates a "snuff of smoke" such as would stream up from a "snuffed out candle-wick." This would also apply using a missing verse, "Its early in the Spring when we round up the dogies....and brand 'em, and clip 'em, and bob off their tails."