A cowboy on a cattle drive generally could not vote from the trail. In the 1880s, there was no modern absentee ballot system that allowed a man to mail in his vote from wherever he happened to be. Voting was normally done in person at a designated polling place, and in many places voting was still a very public affair. By the 1880s, paper ballots were increasingly common, but voters often used party-printed tickets, and voting could still be closely watched.
So if a cowboy knew an election was coming, he might arrange to leave the trail temporarily and get to the county seat, a nearby settlement,or another polling place where he was legally entitled to vote. Though, a long cattle drive could make this difficult or impossible. Trail drives of the era commonly lasted for weeks or months, and the great drives were often headed hundreds of miles north from Texas to Kansas rail-heads. A cowboy who was still out with the herd on Election Day simply might have to miss the election.
There wasn't one universal cowboy party. Location mattered enormously. In Texas during the 1880s, the Democratic Party was overwhelmingly dominant, and many Texas ranchers and other white Southern voters were Democrats. In the cattle country farther north and west, political loyalties were more mixed, with Republicans, Democrats, and smaller parties such as the Greenback Party attracting support. The Greenbacks were particularly interesting to workingmen and debtors because they favored expanding the nation's money supply.
For a cowboy, the right to vote was worth making the trip to town for--even if it meant leaving the herd behind for a spell and riding a long way to have his say.
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Sandra