I have traveld I 10 from Jacksonville thru New Orleans with no problems.Answer
The last I traveled it from Houston to Lake Charles, yes it was definitly open. This was last month.
I-10 is always open .. more or less. There is always construction somewhere. You can check online to see if there are closures in the states through which you will be traveling;
http://www.highwayconditions.com/united_states.htm
Yes, it is always open