Yes. I do it all the time. I have a backpack and ski boots and nobody cares. Even had a backpack, ski boots, and a small duffel bag and they let me on. But backpack and ski boots for sure is allowed.
yes, you are allowed to bring boots and bindings too incase your overweight you can save, always carry on my boots when going on a ski trip because they won't get lost and you will still be able to ski if you find skis to use