I did the same thing. Private road in the mountains in California, but it snowed harder and more frequently. You provide a valuable service allowing you neighbors access as well as ambulance, fire, police, propane and delivery trucks and guests. It is likely that you have a county or state law that requires the road owner or association to maintain the private road in a passable condition.
Since you have a homeowners or road association, you can be paid fees, or be reimbursed for your costs, by the association as part of dues (which you pay too). Make it an agenda item at the next association meeting. Very candidly suggest that winter maintenance needs to be part of the association's responsibility. You can offer a price based on your costs, that you are willing to do it for. Explain that you enjoy helping the neighbors, but your costs need to be considered. The association can go elsewhere if your costs are too high and you need to be able to accept that outcome. You can easily find out what it would cost to contract this work by asking someone that snowplows for fees, and base your "bid" on that. Call around. And offer a fair price.
When I did the plowing, the 7 homeowners split the cost of buying the plow, and annual fees were on a contributions appreciated basis. I could care less about being paid. My neighbors can't afford what my time is worth anyway, let along the cost of operating the rig. I encouraged contributions and supplied a letter showing the cost of plow parts and fuel as a suggested starting point. Everyone (except one consistent deadbeat) paid; and there was the occasional gift of wine or cup of coffee. I enjoyed doing it. I would focus on an annual contribtion rather than hassling all the neighbors for snow plowing money at each storm.
Be aware that a contract (fee basis) plow driver needs to carry liability insurance. You should get liability waivers, or be sure your insurance covers you, especially if you plow driveways or risk hitting buried landscaping, plumbing fixtures or parked cars. You should ask to be reimbursed for your costs rather than be paid for your work. I mean what is 6-hours anyway, its your equipment costs that are bleeding you dry. If you charge a fee, you may change your insured status to commercial and be surprised by no coverage in the event you plow someones roses.