I fly quite a bit and though the TSA or other security agencies regularly open bags, sometimes calling you to witness their inspection - or leaving a TSA love note to tell you that they pawed through your possessions - I never witnessed the airline searching checked baggage. That said, your boots are supposed to be in the boot bag to get covered as part of their ski sports baggage policy. I'm no fan of the the airlines and I think that it should be OK to put other stuff like clothes or tools in the ski carrier or boot bag, but would be on their side if they found a boot bag with only clothes and charged for it.
Southwest not only has a good checked-bag policy but also has the most liberal carry-on policy that I'm aware of. Most airlines specify 45 total inches with no dimension exceeding 22 x 14 x 9 and most, except for United, are usually not too aggressive in checking the dimensions (United does vigorously enforce their 21 x 14 x 9 limit and will make you check a bag that exceeds any of those dimensions).
My boot bag is always a carry-on on the outbound flight, and has my overpants, googles, long underwear, socks and my helmet. My hand luggage is a smaller underseat bag with sundry clothing items that I can't get in the boot bag (underwear, gloves, etc), some TSA-sized toiletries, meds and eye stuff and my electronic devices and camera. If my checked bags - skis and a large rolling duffel with my clothing and all the other stuff needed for a week or so of skiing - get delayed, I have everything I need to comfortably ski on rentals for a day or two. I expect this is the same routine for most folks headed out on a ski vacation.