I use a carry on bag that fits in the overhead compartment for my ski boots. One pair (size 12 shoe) fits nicely with room for gloves and other stuff to be stuffed in around them. I carry a back pack for other carry on stuff that fits in the space under the seat.
I don't think that a boot bag will fit under the seat.
Thats what I do. Boots and one day of ski clothing in the carry on bag in the overhead. Computer and other stuff in my back pack which is also my ski pack w/hydration.