Looping in [tag=273800]@theskidoc[/tag] and [tag=147716]@SkierPT[/tag] , who are both much more qualified than me.
What kind of skiing do you do? If you have a ton of big impacts or fall a lot, that may be way you are sore. Is it a "my back hurts" sore or more of a "this burns because i havent used this muscle in a while" sore?
Whats your gym training plan like?
If your back is sore while skiing it may be you are probably trying to load it in a way that it should not be loaded. worth to look at your form a little bit. Not saying its that but wouldnt hurt to look.
General gym advice, but listen to a physical therapist over my broscience every day of the week.
For core exercises, i would recommend planks, weighted sit ups, ab rollers, and hanging leg raises. Dont forget to do the side version of the last two to hit your obliques.
A stable core? Yes squatting requires a stable core, but other ways to improve core stability- do some bulgarian split squats, single leg box jumps, and dumbell rows with one leg off the ground.
Make sure you have good form other places in the gym. Squatting and deadlifting, while fantastic strength building exercises, can be catastrophic if you dont do them right. Also, make sure you are being well rounded in the gym- That means not only do squats, but do things that work the rest of your entire body. For posterior chain, Hip thrusts, deadlifts (make sure you have good form) reverse hypers, and back extensions. Then even it out with some bench and dips. Dont forget to strengthen hips. Have good form and dont hurt yourself. Many a back issues have been both created and solved in the gym.