What causes cows to have snotty noses?

It can be a bacterial (usually) or viral (less common) infection affecting the respiratory tract that creates phlegm and excess mucus which gets up in the nasal passages. Such infections (such as pneumonia, shipping fever, infectious bovine rhinotracheitis [IBR], parainfluenza-3 [PI3], or bovine respiratory syncytial virus [BRSV]) will also cause the animals to cough excessively because there is also phlegm in the oral air passageways. Such infections or illness affect cattle quite the same way that it does for us.

Other causes, besides certain bacteria (primarily Mannheimia, Mycoplasmas, and Pasturella) or viruses, for snotty noses in cattle is dusty feed, dust by itself from excessively dry conditions, or even moldy feed. Stress from on-the-truck-weaning, transport and/or exposure to dust or pathogens from auction mart stock yards will also cause cattle--especially young cattle, not so much adults--to get sick with a respiratory illness.