Obstructive sleep apnea (OSA) is a sleep disorder where the muscles that make up the back of the throat collapse when asleep, causing reduced air flow to the lungs. Snoring very often accompanies OSA. When I diagnose a patient with OSA, some of them ask me if there are any exercises that can reduce snoring and OSA. There have been studies showing that people who play certain wind instruments can improve snoring and OSA.
Here is an article about a singer that has developed a singing program to be used 20 minutes a day to reduce snoring. In this study, they took people who snored and had mild to moderate OSA. They excluded those with severe OSA or morbid obesity (BMI at least 40). They had them do the 20 minute daily singing for an unspecified amount of weeks. The results showed that snoring frequency, but not loudness was reduced significantly. Also, subjective reports of daytime sleepiness was improved in the singers vs the non-singers. However, the researchers did not objectively measure the level of sleep apnea at the end of the study. So it can not be said that singing improved their OSA. I also can't tell if more of the singing group lost weight, which would explain the decrease in snoring, rather than the singing itself.