Urbanovsky, along with council members Matt Smith of At-Large Position 1, Monica Davidson of At-Large Position 2, Paul Daugereau of Single Member District A and Terry Cummings of Single Member District C, voted in favor of the extension.
Two other council members, Ray Bryant of At-Large Position 3 and Evan Ture of Single Member District B, were absent.
City Manager Kenneth Williams said a new disaster declaration could have been passed during City Council's scheduled Monday meeting, after the current order expires at midnight, but that would open the door for some reimbursable expenses to fall through the cracks.
"One of the main reasons that a declaration's put in place is to allow the city to be reimbursed for all costs in responding, and recovering, to a catastrophic event," Williams said. "That way we are fully covered by having this meeting today."
According to Urbanovsky, the city is still in the process of cleaning road surfaces and working on water-related issues.
"Many individual homeowners have broken pipes in their houses and businesses," he said. "I believe the city facilities or city assets, as far as the City Hall and our buildings, fared fairly well through all of this."
The mayor said he had been in communication with Hays County Judge Ruben Becerra about creating reports to review what could be done better during future winter weather events.
Council members also praised city employees for their handling of events, some of whom stayed at their office or postings around the clock.
"There's lots of folks around us and other communities that did not either have the leadership or just didn't have the systems in place to deal with it, and Buda does," Smith said.
One issue the city was wrestling with was the displacement of residents at Creekside Villas Senior Village Apartments. Officials did not give specifics but said the cause may have been due to power outages or broken pipes.
"I'm hearing that very soon we'll have some of those people back in their houses, and hopefully all of them back here this coming week," Urbanovsky said.