It depends on a few things - how many bags you're taking, how many people you're with, and how fast you can run through that airport! I did an int'l-int'l through Miami in April [Barbados-Miami-Costa Rica], literally ran through the gates after getting and transferring my bag, and got there with seconds to spare. It's pretty hectic
Are you flying from within the US to Houston? Is it possible to have your bag checked right through to Cuba? That's one of the biggest uncertainties - sometimes it's fast and sometimes it takes half an hour.. You should be able to check in for both flights and receive both tickets at the start airport so if you can eliminate the big uncertainty you might just be able to make it!
Obviously this also means no food or bathroom stops though

Be prepared..
Sarah: Little girl, big dreams. Currently living in Scotland
British born, Barbados raised, slowly but surely getting out there. One day..
Next trips: Australia Late March-April; Europe Late June-Mid August