Climbing roses

I'd recommend Pierre de Ronsart, which is white with a pink tinge, and a fantastic fragrance. We have Mme Alfred Carriere but she is a real brute and would soon overwhelm a 2m obelisk unless you took her severely in hand!
I'm afraid I don't know Iceberg or Snow Goose.
Neither of the ones I mentioned seem to have any disease problems that we have experienced.
We have Pierre growing in a fairly small pot and he only grows fairly slowly. We are enjoying our second flush of fragrant flowers at present.

Thanks for sharing that information. I'll give Pierre a whirl!

Yes, Snow Goose is even more vigorous than Mme Alfred Carriere!!! You may get away with Iceberg Climber as it is more moderate. Don't know the variety Bertie suggested but it must be a good one.

Sorry, can't think of a true white small climbing rose myself so this one has me beaten.