Carry on the boots. I've gotten away with bringing a backpack as my carry-on bag and ski boots as my 'personal item.' Check your airline's details, but with WestJet, your personal item could be a laptop, ukulele, chihuahua in a kennel, basketball, a purse and so I brought my ski boots and there was no issue. Then I pack my roller ski bag with all of my cloths, so I don't need a suitcase.
You can get by on rental skis and shitty outerwear, but losing a good-fitting pair of boots can ruin a trip.