I thought the USDA database was a good place to find out about
distribution and invasive status, but... their distribution map says it
isn't in Texas yet ;-). Not a good indicator, Donald - movin' fast!

It lists Tragopogon pratensis as T. lamottei, non-native.

http://plants.usda.gov/java/profile?symbol=TRLA30

The roots are supposedly edible, so maybe the tops would be tasty to
your cows.

>From what I read, it's sporadic in waste places & roadsides, doesn't
sound too pasture/iris garden threatening.

Linda Mann east TN USA zone 7