We have been unable to locate any Texas laws that regulate where or how a marriage ceremony must be conducted. Texas state law regulates certain aspects of marriage ceremonies in Chapter 2, Subchapters C through D of the Texas Family Code.
Section 2.202 sets out the requirements for who may conduct a marriage ceremony in Texas.
Section 2.203 requires the person conducting the ceremony to receive an unexpired marriage license from the couple. After the ceremony, Section 2.206 states that the officiant "shall record on the license the date on which and the county in which the ceremony [was] performed and the person's name," then they must "subscribe the license, and return the license to the county clerk who issued it not later than the 30th day after the date the ceremony [was] conducted."
Marriage laws vary widely across the country. Some jurisdictions may require the couple, the officiant, or all parties to appear in person during the ceremony. This article on Skype weddings from the American Marriage Ministries provides some examples of jurisdictions in the U.S. that have these types of requirements. An attorney could advise you on the laws you must comply with if you are considering conducting your marriage ceremony across jurisdictional boundaries.
According to Section 2.203 of the Texas Family Code, a person may appear at a marriage ceremony by proxy only if they are "(1) a member of the armed forces of the United States stationed in another country in support of combat or another military operation; and (2) unable to attend the ceremony".
Texas Family Code Section 2.002 states that generally, both applicants for a marriage license must "appear before the county clerk". However, Section 2.006 provides an exception for applicants who are 18 years of age or older and are unable to appear personally. In that case, "any adult person or the other applicant may apply on behalf of the absent applicant." The person appearing on the applicant's behalf must provide the clerk with a "notarized affidavit of the absent applicant as provided by this subchapter" as well as "proof of the identity and age of the absent applicant under Section 2.005(b)". Requirements for the notarized affidavit can be found in Section 2.007.
Section 2.006(c) also notes the following:
[…] the clerk may not issue a marriage license for which both applicants are absent unless the person applying on behalf of each absent applicant provides to the clerk an affidavit of the applicant declaring that the applicant is a member of the armed forces of the United States stationed in another country in support of combat or another military operation.
Texas Family Code Section 2.301 discusses the validity of marriage:
Except as otherwise provided by this chapter, the validity of a marriage is not affected by any fraud, mistake, or illegality that occurred in obtaining the marriage license.
Please see the library's research guide to Marriage in Texas for more information on Texas marriage laws.