And can they be rerooted? I've got some rooting hormone, and am curious to give it a try if it's possible.

Nasturtiums don't need staking at all and I doubt the winds broke them off. I'd bet money you have a couple of cutworms under those plants. Cutworm cut the plants off at ground level and feed on the plant roots. Dig down under the plant and I'll bet there is a fat cutworm. I don't think they can be rooted. It is early yet I'd plant more seeds. Soak them overnight first. My nasty's are just emerging from the ground

Nope no cutworms, I dug down a little to double checked. We had winds gusting to 60 MPH and these were the bushiest of all the nasturtiums. I could see them out the window being wobbled to and fro by the wind. Bad luck it is then. :(

I have a few spare plants I grew from seed already I was looking for a place for so I guess I know where to put them.

Just for kicks I put on of them in water and I have little bitty roots now! Huzzah! I'll give it some time and plant it back out later this week. :D

Nasturtiums will root where they touch the ground and are quite easy to root from cuttings as long as you have a leaf joint in the medium/water.