Area below the tub has no insulation and is a source of energy loss even when closed and sealed. The Texas freeze actually froze the water pipe feeding the tub faucet.....I opened it up to allow what little heat we had in the house to help thaw it out. Is there any reason why I couldn't shove a bunch of pink insulation in there? Might be a pain to remove if working on the plumbing but I think it would be worth the trouble.

Sliding the panel off shows plumbing but no insulation. Pipes froze during 2021 Texas freeze.

 

Well we can see the panel but not what's behind it.

They probably didn't put insulation in there because insulation would block the heat from the house (closer to room temperature) from warming the pipes. If you do insulate it, you would put the insulation on the outer side of your pipes in order to allow the heat from the house to warm your pipes. So don't cover them up with insulation. And foam insulation would be better than fiberglass. You should also air seal the edges of your foam insulation with either caulk or spray foam. You want to stop cold air from blowing in onto your pipes. That's the biggest reason pipes freeze. And cold air can still blow through fiberglass.

And next time it gets cold all you have to do is let the water dribble just a little bit. The relatively warm running water (usually no less than ground temperature of 50F-55F) will prevent the pipes from ever freezing.

 

That's an outside wall and little can be done to prevent a freeze, especially if it happens to be a hard freeze. Seldom will you see a sink installed on an outside wall (especially up north). Most common in a kitchen but the pipes will run under the basement and then through the floor avoiding the wall itself. However, sometimes the kitchen drain may be within the wall and the trap can freeze.
My suggestion to be sure of a no freeze situation is have a small electric heater on the ready to blow warm air into the void during cold snap. Tricking water from the faucet is fine, but in the southwest that may be a taboo. You might want to install a decorative grill plate in the opening.

 

Is there anything I can do? Gets very cold in the bathroom even with the panel on.

 

The easiest and non-destructive method is to just use a space heater while bathroom is in use. To really make a difference you would need to do a complete demo and remodel. And even then, you would still feel some chill during a freeze. Being in Texas the operation of space heater should be minimal cost since the freeze does not usually last more than a day and I assume not that often during the winter months. Correct me if I'm wrong.
Of course, for me maintaining a 67-to-69-degree temp in the bathroom bordering and outside would be too hot. But if you're not use to it, it may feel too cold.

 

You need good insulation in the back wall (exterior wall) and some / some more insulation against the back wall behind the pipes. No insulation in front of the pipes so as to block the view of the pipes from the vantage point you have shown. Is there a gap between the bottom of the tub and the subfloor? For good measure fill that with insulation so cold air can't seep or flow under the tub.

Unfortunately I do not know how to install the insulation.or vapor barrier.