Growing Asparagus in Houston. Well, there are easier things like sword-swallowing.
I think the challenge is not enough chilling hours and thus the asparagus crowns/roots don't properly enter dormancy. Although I say that and despite the "climate change", the last few years in Houston have had the coldest winters on record that I remember. Snow used to be a once-every-other-year event, and typically there were only 1-2 weeks of temps in the 30's. The last few years have seen multiple days of snow and 3-4 weeks of temps in the 30's.
I would find out what varieties of Asparagus that Texas A&M is growing here. I believe they've got a patch of Asparagus in Bryan/CS that produces well for them. Maybe check out some of the better (non-chain) nurseries and see if they have some insight.