Short answer: most Houston buyers need far less than 20% down. Depending on the loan, the minimum is usually between 0% and 5% of the price.
Putting down less than 20% on a conventional loan usually means paying mortgage insurance. That isn't a deal-breaker: for many buyers, owning sooner beats waiting years to save 20%.
Plan for closing costs too (lender fees, title, prepaid taxes and insurance). In Texas, the seller can often pay some or all of them. See Can a seller pay my closing costs in Texas?
Every situation is different. A 15-minute conversation and a pre-approval tell you exactly what you'd need for the home you want, before you fall in love with one.