I'm a serious snorer, but there are absolutely some ways to reduce the problem.

One of the very best way to minimize snoring is to stay hydrated. Dry cabin air contributes significantly to dehydration, and so does alcohol intake. You can't do much about the cabin air, but -- and you probably aren't going to like this -- you can avoid alcohol, or at least limit yourself to 1 glass of wine/champagne in the 2-3 hours before you snooze off. Be sure to leave yourself enough time after waking up to enjoy a few more glasses if you like. Equally important, drink loads and loads of water. If in business or first, ask the FA to leave a bottle of water, and be sure to drink from it often.

Finally, if you're a serious snorer you might well have sleep apnea (spelled with a few more vowels if you're European). CPAP machines can do a brilliant job of reducing snoring and giving you sounder sleep. In the past few years, much smaller models of these machines have become available, and it's now realistic to use some models on airplanes.