It may be possible. Also, your horse could have a snotty nose, but when they eat/graze it may get rubbed off so you aren't seeing it... A cough is common also... I honestly didn't know my horse had it 2 years ago until I felt the lump. He hadn't gotten a runny nose or started coughing yet, but he was very lethargic and was laying down a lot and moving a lot slower than he usually would. IT's a very scary thing. I'd have the vet out if I were you. Whether to medicate or not is very contricted even among vets. One vet told me to treat with penicilin, another told me to just wait it out and clean my barn with cleach everyday until the sickness had run its course... Call your vet.