I was just at the homestead this summer... didn't pick up on the idea of Carrie's health being affected.
As you say, she was always described as being sickly, so I don't know that you can blame the winter for her childlessness. She did live to be pretty old, so she couldn't have been that badly affected.
Speaking of which, I wonder how much the childlessness was by choice as opposed to health. Or at least I'm sort of skeptical that the childlessness was caused by the conditions. The German side of my ancestors were in the Dakotas during that time and they had kids. Furthermore, the Ingalls girls all lived relatively long lives.
I have often wondered why Laura only had one child and Carrie and Grace never did. It seems pretty unusual for the time.