Adventure is nothing but a romantic name for trouble.
~ Louis L'Amour
When you stop and think about it, L'Amour is perfectly right. What does the typical definition of adventure entail? A journey through an unknown land? An obstacle to overcome? Battles, perhaps, or just uncertainty as to the future? In plain English, trouble. By that definition, I guess you could call an adventurer a person who expects trouble but doesn't mind it—or even looks forward to it.
Once you've looked at it that way, the reverse is true too. Anything out of the ordinary that you might typically regard as trouble could be an adventure. When the power goes out and you have to light the stove with matches and work by lantern light, you could call it a hassle, and then again you could call it an adventure. When a road is closed and you have to take a detour that leads you down unknown, bumpy dirt roads that look as though they haven't been traveled for years, that's no nuisance—that's an adventure. When your garden shed blows over the fence into your neighbor's woods (I am still speaking from experience here), there must be some part of you that feels it's an adventure, in addition to being a disaster. I must be a bit of an adventurer at heart, because I can't help feeling a bit of gleeful relish in situations like these—if only inwardly, in consideration for the feelings of other people who might not be so amused.
When you're dealing with the Western genre, the kind of adventure that first comes to mind is likely the one established by years of movies—the gun duel on Main Street, the high-speed chase across the prairie, the shootout in the rocks. While these things undoubtedly did happen (and good stories can be made of them), I think that writers of Westerns—or any historical fiction set in a newly-settled part of America, really—shouldn't feel limited to these familiar incidents. There's a much broader range of incident to draw on. You have only to read some first-hand accounts of pioneer life to realize that. When you lived two days' journey from the nearest settlement, travel of any kind was an adventure; a traveler stopping by was an adventure (especially given the variety of people you might meet on the frontier). Dealing with weather or just putting food on the table could be an adventure; a social gathering was high adventure. There's a wealth of inspiration in that multitude of quirky, interesting and memorable incidents from frontier history that weren't flashy enough to make it to the big screen. My own advice to a historical/Western writer would be this: read a lot of those personal accounts from history, to get a flavor for the times, and then use your imagination. Don't think that an outlaw with a black hat and two guns is the only viable source of Western excitement (however handy he may be on occasion). Because adventure is out there—everywhere.