Here's my 2 cents on 2 very practical ways smoking affects trumpet playing.
It's hard to play the trumpet if you can't breath. With smoking-related COPD, your ability to exhale is compromised. It's hard to play the trumpet if you can't blow. If you smoked a pack a day for at least 20 years, it's very likely you have COPD. If you are over 40 and have smoked a pack a day for at least 10 years, it's also very likely that you have COPD.
It's also hard to play the trumpet without teeth or a healthy embouchure. Smoking increases your risk of tooth decay and periodontal disease. It also delays wound healing, increasing the time to cover from cuts on your chops, oral sores, or embouchure injuries.