I use "cowboy culture" for lack of a better term, but I don't necessarily mean actual cattle drovers. I mean (to the extent the following examples even properly define the "Old West") the boomtowns and settlements, the six-shooters and ten-gallon hats, the conflicts with/fear of natives, and the trade with more cosmopolitan areas. I'm relatively aware of what was going on in the mid-late 19th-Century in the Southwestern U.S., but how far did that culture extend? Would it be similar in a rural town in, say, Cuba?
I can speak for Canada a bit, having grown up in a cattle town. We have plenty of cowboy culture, especially in my home province of Alberta.
For most of the our province's history, our main industries were agriculture and ranching, and even today, they are second only to oil and gas.
Although a lot of the cowboy culture has faded, many of the values remain. Rodeo still thrives in Canada, centred around the Calgary Stampede and many other rural rodeos. We also have our own rodeo sport, chuck wagon racing, which I actually have a lot of family competing in. It's the main event here, but to my knowledge, has never caught on elsewhere.
For the most part, Canada's cowboys resemble the American variety. This is because borders were basically meaningless back in our frontier days. One big difference might have been gun laws. In Canada, the North West Mounted Police (the first mounties) enforced strict laws on where guns went. It was illegal to carry a gun in most towns, especially during the Klondike gold rush. Another difference was the lack of Mexican cultural influences, slavery, and the American civil war. The first cowboy in Alberta, the man who brought cattle to the province, was actually a freed slave from the states named John Ware.
The native population was never as violent as it is depicted in the states. They were relegated to reserves fairly early. When the Calgary stampede first opened, the natives were actually included in the festivities and events. Before that, their admission into the city was very regulated.
The gold rush in the Yukon and the whiskey trade brought a lot of 'old west' culture to Canada as well. Canadian prohibition was never as strict as it was in the states, so lots of boot leggers out west here smuggled whiskey and rye across the border to serve Americans.
Smaller populations and in turn less government and industry meant that the cowboy era in Canada started and ended a little later than in the states, but it was basically a branch of the same tree. It was all the frontier 'old west', and then somebody drew a line through it.
the conflicts with/fear of natives
I'm at a loss for good citations right now, but the Yaqui were caught on the border between Mexico and the US and their dealings with the people and governments of both would probably be close to scenario I think you're thinking of.
I know Mexico had it's own share of boomtowns, especially with Chinese immigrants but I don't that really fits with the "Old West" you're thinking of. Cuba, as I recall was more focused on large plantation operations and lacked the available/cheap land and unexploited resources that would have drawn people out west.
I'll have to see what I can dig up when I get home, because I know I still have a book with some information about the US/Mexico border and indigenous tribes somewhere. I'd argue at least some of the "Old West" as we'd know it, doesn't exist outside of popular retellings and legend, but I'm not an expert.