I second the comment about the hallmarks being crucial to id the maker.

I’ve been a silversmith by trade for years though, so there are a few things I can tell you about the materials used.

This looks rather modern to me. The soldering looks made with an electric welder/electric soldering iron, as opposed to any fire/torch methods. I’m not familiar with soldering with welders so I’ll leave it to others to confirm. However, if true then you can start estimating the maximum age for it. I’d be surprised if it was over a hundred years old.

Next is the decor. The patterns are made with punching tools, also called chisels sometimes. It’s not a particularly elaborate or sophisticated pattern or execution of technique so whoever did this wasn’t working under any big name smiths. It gives off the feel of a hobby or quickly made artisan’s craft. It’s neat an the result looks good but it’s not sophisticated at all. Going back to the chisels used, these also feel relatively new to me. The round punches are too perfect but don’t seem to have been hammered repeatedly, which means the round tool used was probably made with a bur on a drill, just like I’ve made mine. If it were something really old the punches would be showing more signs of imperfections especially since whoever made this only hammered once or twice each punch, not enough to cover up anything. Since the marks are too round and perfect, I take it as another sign of being relatively new.

My two cents

By a cow.

Unless you can find hallmarks on it, it’s specific provenance would be difficult to determine. You would be best served if you found an appraiser that deal with this sort of item to give the best info on your drinking horn.

I’ve never heard “tinhorn” used to refer to an actual object - what an interesting twist language makes through different eras and groups.

The only definition I’ve known is the “inexperienced gambler”:

tinhorn gambler

A cheap, small-stakes gambler who boasts and dresses ostentatiously to seem more successful or skilled than they really are. An allusion to the dice game “chuck-a-luck,” which features a chute, called a “horn,” from which the dice are dispensed. More high-class leather horns were often substituted with makeshift tin ones, and thus cheaper, lower-stakes gamblers were known for their tin horns.He always wears the same three-piece suit and slicks his hair back like he’s the Great Gatsby when he comes in to play, but everyone knows he’s just a tinhorn gambler who taps out after losing a couple hundred bucks.

https://idioms.thefreedictionary.com/tinhorn

Not to say you’re using the term incorrectly, at all, just a neat observation about how language drifts.

Looks like an elephant made the tusk.