The property must have been the surviving spouse's residence homestead at the time of the veteran's death and remain the surviving spouse's residence homestead. To receive a disabled veteran exemption, you must either be a veteran who was disabled while serving with the US armed forces or the surviving spouse or child.Bexar County Property Tax Exemption. Applications for exemptions must be submitted to the Bexar Appraisal District. To receive a disabled veteran exemption, you must either be a veteran who was disabled while serving with the US armed forces or the surviving spouse or child. Texas offers a partial property tax exemption for partially disabled Veterans. Did you know there are property tax exemptions for seniors, disabled veterans and Gold Star Spouses?