So, in my opinion, A Hospital, as long as it provides services to the public for a fee as it's main purpose, (Hospitals are businesses... you pay them for services.. remember that!) is NOT included under the 46.03(a)(1).
I agree dicion, it doesn't fall under 46.03(a)(1), but it
does fall under PC 46.035(b)(4):
"Sec. 46.035. UNLAWFUL CARRYING OF HANDGUN BY LICENSE HOLDER. (a) A license holder commits an offense if the license holder carries a handgun on or about the license holder's person under the authority of Subchapter H, Chapter 411, Government Code, and intentionally fails to conceal the handgun.
(b) A license holder commits an offense if the license holder intentionally, knowingly, or recklessly carries a handgun under the authority of Subchapter H, Chapter 411, Government Code, regardless of whether the handgun is concealed, on or about the license holder's person:
(1)1......
(2)...
(3)...
(4) on the premises of a hospital licensed under Chapter 241, Health and Safety Code, or on the premises of a nursing home licensed under Chapter 242, Health and Safety Code, unless the license holder has written authorization of the hospital or nursing home administration, as appropriate;......
BUT:
"(i) Subsections (b)(4), (b)(5), (b)(6), and (c) do not apply if the actor was not given effective notice under Section 30.06."
If you don't see a valid 03.06 sign, then you can carry. But if they ask you to leave(if they find out or know) then you must as they gave proper notification.