Synthetic is better and is great in air cooled engines. The thing about oil is that you can read about it all day, and get a hundred different opinions. You will get a ton of people telling you what synthetics they use. Myself and others here like Rotella T6 5w-40 for diesels which is also JASO MA certified. (I run it in my Jeep, Volvo, Foreman, 1500, and lawn mowers) It's a great oil. Others will say use amsoil or royal purple. It's all about preference really because they are pretty similar.
The biggest benefit of synthetics is higher heat resistance, which prevents breakdown. Conventional oils have long chemical chains that break down in high heat and pressure. This is key to air cooled foremans because they have both high heat, and the oil is used in the transmission which gives you that high pressure and shearing power. Synthetics do not need these chains to stay thick so they are far more superior. As you use your foreman, heat and pressure break that conventional 10w-30 down, it very quickly becomes more like 10w-20 or lower. You won't have that problem with synthetics.
Synthetics stay thin even when in below freezing temperatures (sounds counter productive, but it's all about oil film in the end), this will allow for faster cranking speeds and will help with cold starts, also enhancing overall flow of oil which drops your engine wear.
Synthetics maintain oil film for longer periods of time. So if your quad sits for weeks at a time, that means you have less starting wear for that short period of cranking with no oil pressure because of the preservation of oil film. This is minimal but still a benefit.
The additive packages are also higher in the diesel products which will help keep your engine insides clean. You can make your own synthetic blend without any issues as well. You could mix GN4 with T6 in any precentage combination you want and have a good blend to give a trasition period. This would be so you dont wash out too much gunk too quickly. Although I really wouldnt worry about that being an issue unless it was really abused.
I can explain oil weights too if interested.