Yes, purchasing in cash is one option, and the HELOC is the easiest if you want leverage.
Then you're dealing with managing properties in other countries. It can work, it's just not my preferred method, like I said, I prefer notes.
And, of course, a vacation home is not an investment, it's almost always a poor financial decision based on emotions rather than numbers.
Certainly getting other people's experiences is good, but don't let it stop you if you don't find exactly the anecdote that applies to you. Too many people want "just one more piece of information" and never pull the trigger.
There are tons of foreign investors coming into the US right now (lots of Canadians and Australians, specifically, here in Vegas), so I know that it's done all the time.
Do you not hold any investments outside retirement accounts? I almost exclusively invest outside of them, and deal with the taxes, because the avilabability of returns and lack of restrictions on what I can do make it worth it (regarding real estate - my equities are held within taxable accounts).