Is it proper to propose a thesis collaboration to a professor you don't know? I am a master student at one of the best universities in Europe. As I am studying finance, I would like to have an experience in the US or London.

I will have to start working on my master thesis next year, and I would like to use this opportunity to go abroad to an important institution; my idea would be to write to a professor and ask him if he would be interested in co-supervising my master thesis; I would not be paid of course but would enjoy the experience.

Is this considered proper or is it rude / weird?

Of course I will look at professor that works in an area that interests me, but I probably wouldn't be able to specify a particular topic right now (I will do an internship next semester where I plan to find a particular problem to work on, but I don't know yet). 

The start of this thesis would be next year, but I think I should start contacting people now for this kind of proposal.

So in conclusion is this something that happens? Should I really do more research before contacting a professor? How can such an interaction be phrased?
A few students work with professors from another department of the same school, and in a few cases, their advisor has recently moved schools, but mostly most students are advised by professors in their own department. 

In my limited experience, professors are interested in supervising thesis projects only when they have a preexisting relationship with the student.When i was a student, I once asked a professor to advise my master's project and was told, "no, you have to take my class first".

It's more than helpful to cultivate relationships that will support your work, but when you cold-call people, avoid asking them to trust you or commit to work with you.