I don't think you did anything wrong. It was a really wild spring with unusual weather. The roses wanted to grow very early in the season, and there's no way to stop this.

This is one of those times when things happened beyond our control...

Hybrid Teas can be more vulnerable to cane dieback than other types of roses, so there could potentially be greater losses with them, in a bad season.

We actually go through this every year in the Connecticut river valley--the weather warms up nicely, the plants start growing, and winter returns to kill the new growth. My solution is to take out the old and dead canes completely--often using a pruning saw. Next, I'll move any roses that need to be moved--this year I moved a cherry tree and the roses surrounding it. With 200+ roses, by the time I've finished this, it is often safe to prune the roses. But, this year, I pruned everything lightly, leaving the canes long. By leaving the canes long, there are dormant buds lower on the cane that emerge if the new growth is killed by the frost. We did lose one HT, the first in years--it was on Dr Huey and had Ph issues that weren't corrected in time for it to gain enough reserves for winter.

I did some pruning early too but I never hard prune just for the sake of it. If a cane is green and the pith looks healthy I leave it long. If it does start to wither later I can always take it out then. But you can't put them back once you've cut.

They may not have made it in any case but don't count them out just yet. It's still pretty early in the season and we haven't had all that much good weather. I've had roses come back that I was sure were goners because I never got around to digging them out. When I did get out there to do it they had sprouted!

If they are own root, you should see some rebounding soon.

I too experienced the warm summer weather in March. But I ignored it and waited until Mid April. As a result I'm pruning just a little bit plus any damaged or dead canes. Most bushes are fully leafed out and flowering now.
Hope you learned not to get an early start when Mom Nature can't make up her mind. It seldom hurts to wait until the proper time.
While pruning now, I find some frost/freeze damage but with all the foliage on my bushes, removing it isn't harming anything.
I don't fertilize until the first bloom to avoid a push of tender foliage.
Seems we warned everyone in mid March not to get carried away. Winter wasn't done yet.

I pruned some of my roses early and some late, and I've got roses that are struggling after the late frosts in both groups. I've got other roses that are huge and flowering now which is the earliest ever. I'm thinking that I'll replace some of the ones that aren't doing as well as there are a couple that have never recovered well from winter and limp along every year.

Based on all of your feedback (much appreciated!) I think that perhaps some of my roses may be just a victim of the crazy weather. I won't prune or fertilize quite so early next year, but I'd like to think that doing both wouldn't actually kill my roses. None of my roses (except John Paul II -- the star in my rose garden) are quite a vigorous right now as they were last year when the weather wasn't quite so crazy.

I'm sorry, but I disagree with krista_4. It is wrong to fertilize within two weeks after pruning. You should see a couple of inches of growth on each rose and some reasonably effective leaves that have popped open. Fertilizing before that encourages growth too soon and sets them up for a quick kill in late frosts. That's a standard precaution against "crazy weather."

Note that there are some roses - despite what your county extension agent may say about hedges/bushes - you can kill a rose by pruning too agressively. Usually, the classics are most sensitive to this: Peace, Queen Elizabeth, Mister Lincoln, etc. Don't go hog-wild with those varieties or similar. You may be disappointed. Peace and QE are infamous about hating hard pruning. For all the recent stuff, I say hack away, but not for those. ;-)