I would highly suggest you go.
As you say in the title, it is a once in a lifetime trip.
And, although I don't know exact statistics, I think there is actually a rather large part of the population of the USA which has never left Northern America or even the USA itself. You should take the chance.
And Europeans places are interesting. You'll make new friends and whatnot, and it'll be cool to have international friends when you return to America.
Not to mention, it looks quite nice on a CV (Résumé for Americans) to say that you have lived abroad and are capable of working out of the country.
It if it's free travel across and I'm assuming accomodation, then it's perfect.
And it's only for half of a year. So even if you dislike it, you'll be back home soon, and if you enjoy it, it'll probably be over before you know it and you'll be wishing you didn't have to go back so soon.
As for the weather, it's much like most of Western Europe in the Autumn.
A bit cold and rain is common.
If you watch the weather reports for most western european countries you'll see you get a lot of rain and such that comes in from the Atlantic, hits the UK and washes across France and Belgium and Germany and whatnot.
And if you're there into the Winter you might get some snow too.
I say go for it, give it a try, see if you enjoy it and have a good time.
If you don't like it, then you've not really missed out on much.
And it's all a nice experience.
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