First, thank you for everyone's information. I appreciate info from people who have been or were just there. Feet on the ground information, if you know what I mean.
Strangely enough Hornlihuette being closed is why we are going to Zermatt this time. It turns out that while Hornli is closed for refurbishment and an addition (a cube dormitory area it looks like although I have not seen the actual plans) they have created a new thing: Basecamp Matterhorn. They built it, opened it on July 14, 2014, and will close it on September 14, 2014. Two months.
We have been planning to go to Hornli, and then to Solvay, but don't want to with a young child--at least to Solvay right now. It came up that Basecamp Matterhorn was being built on the Hirli and we decided to try it. Couldn't resist, really.
Check it out, especially if you are going to be there in that window of time:
http://www.hoernlihuette.ch/base_camp_3.html?directlink=basecamp
Thanks again!