IMHO you and your RTC would be better off if the cat went inside for the winter. One can get a cheap above ground pool from Walmart for $100 and throw rubber liner in it for another $100 or less.
Or you could build a plastic greenhouse / enclosure to protect your existing pond from the elements. Or at the very least build low walls e.g. of cinder blocks, lay down a few cross boards, etc. and cover the pond with plastic / tarp.
If you can't do either, I'd donate the cat to whoever can take care of it asap.
If I were to make the cave, what should I set the temp as on the heater inside the cave. And do you have any reccomendations on heaters? So far I've only seen affordable 500w heaters. And considering the dimensions of the cave what size heater should I use 1000w? Or 500w? The cave will have 3 acrylic panels.( 2 side panels, and a roof panel)
My 1000 W heater was on 24/7, set at the highest temp so it doesn't shut off.
I didn't read your OP carefully enough the first time, sorry. I thought the heater will be inside the cave with a heater guard. If it is outside, it may not do what you want at all - the warm water will rise and the cold water will keep replacing it on the bottom and in the cave in a process called convection.
It'll be like installing a fireplace on the roof of your house - it won't do you much good.
Just laying the heater in a heater guard on the bottom without any caves has a better chance to work but even so this is a huge gamble. I again recommend to rehome the fish asap or risk losing it.
One can get cheap heaters 200-300 W from almost any LFS. They run $20 or some such.