Good news! The vet came out this afternoon to check out Cool. While it looks like he does have a little bit of an infection maybe going on, he doesn't have any lung noise (no crackling, no wheezing etc.) and the vet thinks that his illness is actually part of his allergy problem.
We used a different vet than our usual because she is out of town until tomorrow, but I think it was actually good to get a fresh opinion, and the vet that did come out is one that I've had some experience with and I do respect his opinions. He checked Cool all over and listened to his lungs, like I said, no lung noise, no swollen glands, no pain anywhere and his temperature was 99.8 so back within the normal range, even if it is still slightly high for Cool's "normal." This vet went a little more in depth with me about the allergen process. He said that he would prefer to call Cool's condition "airway inflammation" versus just "allergies" as allergies is such a broad term. While it's not technically COPD, Cool could potentially develop it in the future. Horses with allergies can occasionally go through phases of airway inflammation, which is what Cool has been dealing with lately. Apparently it is not uncommon for these horses to have a mild cough, some nasal discharge and a low grade fever (102 is considered "low grade") especially with the crazy up and down weather that we have been having lately. A 10 day round of antibiotics should help to clear up his airways but the vet doesn't believe that he has anything contagious like influenza or anything. I'm going to continue to take Emmy's temperature just to be safe, but he vet thinks that everything should be alright. The vet also told me that I had beautiful, clean stalls and to keep up the great work with managing Cool's environment (ammonia is REALLY bad for horses, especially those with allergy/airway problems; it keeps the respiratory system from being able to clear itself) so yay for that!
I'll keep you all posted, but it seems like Cool should be just fine and that this is just going to be something that we have to manage carefully from now on.