Not sure about Texas, but I have years of experience doing that in Nebraska (very conservative state even requires a title for a Model T!). I’ve driven many classics (1954-1959 Buick’s and Chevys mostly) as daily transportation (work, shopping, etc from rusted out hulk to almost trailer queen). As a child of the 80s to me I got a much stronger respect for the engineer teams building cars that really are more like suvs today then cars. I’ve never had any issues with law enforcement (in fact they intentionally leave you alone, and are less likely to give you tickets (ask me how I know haha). I drove all over the state, blizzards, downpours, everything. The cars were ALL in as built condition (unmodified) and actually got a lot of attention (the ones not rust buckets 😂). As long as you have turn signals or use the hand gestures for signals, a brake light, and headlights you are fine. Being able to hop in your car and go whenever wherever you want is the whole point of having a vintage car. Car washes, part supplier, etc are there for a reason, unless it’s a very, VERY rare or valuable car, take it to work, shopping, etc whenever and enjoy it. Makes the whole driving experience more rewarding to. Hope that helps 👍