How large should the rose grow? Do you require it to bloom more than once a season? Must it be fragrant? How large must the flowers be, and must they be doubles (or are semi-doubles and single white flowers also acceptable)? Must the flowers be pure white?

I am not sure how it will be in your zone ,but here in 6B Iceberg is always naked from BS from mid June on, unless you spray it regularly. It is a pain to spray climbers in my opinion.
Thre are some better options, I believe.
White Cap, Ilse Krohn Superior (mostly once bloomer, but very hardy), White New Dawn. There are also many onceblooming roses that will work, like Mme Legras se St Germain, Mme Plantier, etc.
Olga

Well, I guess I will probably leave out the Iceberg! lol I had my doubts about that one. I have also bought ramblin red, and william baffin which I will stick to. I was trying to find a pure white rose, a climber, to go with the red and pink of the other two. I don't really care if they are fragrant, as I can't smell very good anyway (sinuses always clogged up lol). I have a 6 ft high, 20 ft long trellis that I will be planting these on. Or do you think just the ramblin red will fill it in enough? I hear that both ramblin red and william baffin can get pretty long.

Thanks,
kentstar

HelpMeFind lists a white climbing rose named Lace Cascade that appears to meet your needs. I'm not personally familiar with it, but if it actually performs as stated, it may be of use to you.

How would Sally Holmes do in your area? She is a smashing rose when in full bloom, and HMF says she is hardy to zone 5b. I used to not like her so much because I'm not a white rose person and I didn't care so much for singles, but I have come to appreciate her masses of blooms. She's a classic. Someone in your area can comment on whether this is a hare brained idea for reasons of hardiness, disease, etc. :)

-Greta (a long way from you in Portland, OR, zone 8)

They both look beautiful (Sally Holmes and Lace Cascade), but I am looking for a white climber that is actually hardy to zone 3 or 4. I want my zone to be "within" the hardiness range if possible. That way I can be a little more certain of it surviving these chilly Ohio winters. For example, if the rose's range is zones 3 to 8, my zone is 5b and within that range. But, I am finding it very hard to get a "true white" rose that is THAT winter hardy lol.

The "climbers" available to you that are that hardy are probably going to be once-bloomers. You may have more success hunting in HelpMeFind among the shrub and species roses. It's not unusual for a "shrub" to be large enough to be a "climber" if you train it the right way. Here's a candidate (again, not one I have personal experience with): Créme.

I have Lace Cascade. It has climbing iceberg in it's parentage. It looks a lot like iceberg, is long and lanky. Has two or three good flushes. Not fragrant. I don't know how it would be in zone 5. Blackspot here in the PNW is not as good as iceberg. It gets pretty bare.
Kathy