YOU may not need the heater, but your windshield will. You will have virtually no defog / defrost available, if the air being sent up to the windshield is not heated. And I am pretty sure that Texas gets heavy dews, and even frost on occasion. Obscuring your forward vision with an opaque windshield is a recipe for trouble. If you feel you must remove the core, then put some other kind of hot air blower up there to keep the glass clear and heated. There are some nice electrical ones for light to medium duty jobs.
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  As part of my project I'm planning to take out the rear heater core and now
that we live in texas i'm considering removing the front as well. I'll be
taking off the dash to fix the vents so i'll be right there already.
Here's my rational:
1. I don't want to spend the time or money on replacing hoses and the
exchanger to ensure the refresh is complete.
2. It's just another potential failure point that i'm not sure i'll
actually need.
3. compared to the midwest, texas just doesn't get cold enough to warrant
having heat. i'd rather bundle up if it's a little cold.

Evan Mac Donald

1984 Wolfburg
1985 GL 7 Pass.
1991 Carat Weekender
1972 Chevy P/U
1993 Bonneville