Some do, some don't.  It depends on the needs of the association.  One option that many associations use is to charge one rate for summer people and another for year-round residents.  That way you are not asking those who only use the road in summer to pay for a service that only benefits those who stay for the winter. 

Other associations have enough members so the extra cost of snow removal, spread out over all the members, is not overly burdensome.  In one case where summer residents objected, it was pointed out to them that for year round maintenance, the cost per member was comparable to what it would cost just to plow a driveway.  It also gave them the option of using the road any time, plus it provided better security because the year-round residents kept an eye on the whole neighborhood. 

If your association is "statutory," set up under 23 MRSA 3101, the statute only requires, " The determination of each owner's share of the total cost must be fair and equitable and based upon a formula provided for in the road association's bylaws or adopted by the owners at a meeting called and conducted pursuant to this section." 

The Courts have said that any formula is fair and equitable so long as it is applied equally to everyone. So you could change your bylaws to cover winter maintenance, and use either the formula that everyone pays the same, or the formula that year round residents pay more, and as long as you are consistent about applying your rule, it conforms to the law.  But my guess is that since you say most are summer residents, they would be more likely to approve the first option.

I see why you have a problem!   The summer residents outnumber winter residents, so their will is most likely to carry on a vote.  I still think your best bet may be to devise a dues formula that fairly reflects who uses the road when. i.e. divide the cost of road maintenance (not counting snow removal) by the total number of residents, and that is the dues payment for summer residents.  Then divide the cost of snow removal by the number of year-round residents, and add that to the cost per member of road maintenance to get the dues payment for year-round residents.  The summer residents are less likely to object to winter maintenance if year-round residents bear the brunt of the cost of snow removal.  That wouldn't necessarily give you increased funds for snow removal, but it would give you some enforcement structure for getting all of the year-round residents to share the cost of winter maintenance. Maybe you could also have an in-between option where summer residents could pay a bit more if they want to be allowed occasional winter use.  The closer you can tie the amount of use to the amount of the fee, the more fair it will be, and the happier everyone will be in the long run.