Is this some sort of rich mountain-goers joke? I've never been burned on the ski hill, even as someone who burns very easily

Skill issue

If spending a few hundred bucks sounds like a big deal to you then maybe skiing (or pretty much any hobby) just isn’t for you. This is a luxury activity after all.

Like any hobby it takes time, money, gear, and sometimes even training if you want to succeed.

As for injuries, anything is possible when participating in a physical sport. However most injuries are going to come from doing reckless shit. Start slow on easy hills and work your way up. Experience is what keeps you safe. There’s no reason to get injured unless you’re not using good judgment.