LOL!! Ya got me!! First a north facing balcony limits the choices although there are definitely a few that will tolerate a shadier location. But "up all year", "screening the wind" AND able to grow in a container is a seriously hard combination to come up with.

It is certainly not a large flowered cultivar - none of those will be up all year - and it is not all that common (you will most likely need to mail order) and it may be marginally hardy for you but I'd consider Clematis fasciculiflora. It is evergreen, of small enough stature as to be happy in a reasonably sized container and rather shade tolerant. But it has small, nodding cream colored flowers that bloom in winter and is only rated to zone 7. Clematis, even the evergreen forms, are not known for wind tolerance. Winter wind and marginal cold temperatures does not spell great success IME.

lol, thanks for your answer. I did not know about clematis not liking wind...well... I did not know a lot of what you said. I'm glad I asked.
Another question... If I took out the "up all year" aspect... what are my chances of growing a common clematis successfully?

That simplifies things considerably! There are lots of smaller growing vines well-suited to a container on a balcony. And many will be happy in a fair amount of shade. The fact that they lose foliage and "die back" during the winter when winds tend to be the most brutal is an advantage.....but not so good when it comes to providing privacy. May have to get that from another source :-)

Unfortunately due to pruning requirements ( not for life but for best performance) most Clematis make lousy privacy screens....they also don't climb standard slanted wooden slat lattice very well. I found this out the hard way, after DH built yards of such trellises....

Okay, thanks for your additional info... lol, each time someone answers me, I have even more questions! They don't climb normal wood slat lattice!? I never knew that. What do they prefer? wow, I've got more to think about. --------Soooooo, if I was going to try anyways... a question from gardengal48's post, what would be a "smaller growing vine"? I keep hoping you'll say something very common like Nelly Moser. Butttt, knowing me I've got it all backwards. lol.

Nelly is not the most compact of vines but she could work :-) I'd look for a book at your local library (or online if you prefer) by Raymond Evison titled Clematis for Small Spaces. Evison, who is a very well known clematis hybridizer focusing in on smaller, free-blooming container or patio clematis, presents all manner of smaller growing clems for exactly the sort of restricted growing conditions you have. Lot sof pics, lots of names of potental choices!

If you have string of the same color as your trellis and weaving through the trellis, the clematis will climb that. Wire grid panels will work well, but aren't very decorative. Clematis need some thing smaller in diameter than a wood trellis as they climb by wrapping the leaf stems (AKA petioles) around what they want to climb.

I have Clematis for Small Spaces and will second gardengal's recommendation - good info and photos.

Thanks everyone, I think I will put some twine running vertically up the lattice, and look at the garden centre's options for clematis... and pick the shortest one, that has big flowers... I guess I'll wing it. (My library doesn't have the book you mentioned, it just has Clematis for Everyone by Raymond Evison. But, I'll pick up that one anyways)