Did those strange shoots have flowers that looked like White Dawn? (Those flowers needed to look almost exactly like this to be White Dawn flowers.)

If the flowers didn't look like that, then you probably have a grafted rose that sent forth new canes from the rootstock, and that rootstock won't be White Dawn, but some other rose instead.

White Dawn is an awkward grower ... you did a great job of describing it.

The idea with a climber is to encourage the length by not cutting the tip of the canes. You shorten the laterals that develop along the cane after they bloom (not what you have yet, it sounds like).

Your rose is still new, and it will develop more for you this year. As it matures, it will be more likely to develop new canes. Here's my example: Last year was the second year in the ground for my Climbing Dainty Bess. The first year, I didn't get much from her ... she grew, but didn't show any long, climbing canes. Last summer, she shot this huge cane practically up to the sky. That thing is WAY over my head, and I was thrilled. I expect more of that this year. It sounds like your White Dawn did the same thing.

HTH,
Connie

White Dawn is also marginally hardy in the north. I grew it for about three years and it barely amounted to anything, let alone a climber, as each year it was severely winterkilled. You may have difficulty keeping enough canes alive after each winter to grow out enough.

Sounds like my Westerland rose! I planted one last summer own root though. It shot up ONE long cane that grew about 8 ft tall, but not one bloom. No other canes but that one, in the space of 2 months! Weird! I am also hoping that this year will see more canes from the base, and so far I think it is growing them. I went out and took a close look at the rose at the base and there are two tiny nubs right near ground level starting to come out. Yay! I do not prune a main cane, except this year the ONE main cane had some small breakage at the end, so I did prune that off. Otherwise, just like hartwood said, just prune laterals only. You might want to check out Paul Zimmermans video on how to prune a climbing rose.

Here is a link that might be useful: Pruning and controlling a climbing rose

I wouldn't do any pruning at all for the next two years to allow it to mature. Climbers can take that long (or longer), it needs to grow roots first, and it needs the existing canes.

Do keep an eye on the blooms, though. If it doesn't bloom or if the blooms look like these, then as york_rose said, your White Dawn has died off, and the rootstock Dr. Huey is now growing.

I think he said the rose is own root, so it can't be Dr. Huey. As others have said, with any climber, the first two years do not prune anything, with the exception of dead or damaged canes. Just let the canes grow and train them, if possible, to a horizontal position. The flowers will come from laterals off of these main canes, not the main canes.

Yes, last year's blooms did look like those...the same as the blooms on the original canes. These two shoots are from above the graft, if the graft is where it looks like it is, below the original canes. Should I try to find a way to post a picture?

Okay... so just let it go then. When you all say keep it horizontal...uh... any suggestions? right now it's laying on the ground, six feet off to the right of the plant, looking really goofy. :-)

It's a climber, what did you plan to have it climb on? You could tie it to a fence or wrap it around a pole. Or you can get a trellis and attach it to that.