Ask Mr. Smarty Plants

Deciduous woody vines [e.g., Parthenocissus quinquefolia (Virginia creeper), Wisteria frutescens (American wisteria), or Vitis mustangensis (Mustang grape)] will lose their leaves in winter but the woody stems of the vines will remain.  Unless something happens to kill the plant itself, they should re-leaf on the same woody vine in the spring and add new growth as well.  Herbaceous perennial vines [e.g., Passiflora incarnata (Purple passionflower) or Matelea reticulata (Green milkweed vine)] will die back completely in the winter leaving vine remnants that will need to be removed.  The vines themselves will grow anew from the ground in the spring.  There are some vines that are classified as "herbaceous to woody" [e.g., Clematis texensis (Scarlet clematis)].  In the case of these, you would need to remove the dried non-woody parts after they die back in winter.   Evergreen vines would, no doubt, be less trouble to maintain.   You would probably want to remove any dead sections, but, hopefully, there shouldn't be much to remove.   Here are some recommendations for evergreen vines that do well in Austin:

Lonicera sempervirens (Coral honeysuckle)

Bignonia capreolata (Crossvine)

Gelsemium sempervirens (Carolina jessamine)

You can search for perennial native Texas vines yourself by doing a COMBINATION SEARCH in our Native Plant Database by choosing "Texas" from the Select State or Province slot, "Vine" from Habit (general appearance) and "Perennial" from Duration (lifespan).  If you want to see only evergreen or semi-evergreen vines you can select those under Leaf Characteristics.