I did the trail in '06, a high snow year. Left KM June 14th.
First - it’s too early to tell what the rest of the winter and spring will hold. Perhaps it will turn out to be an epic snow year…then again, it might stop snowing in February. I’d suggest: Wait and see…plan to replan…be flexible and adaptable to the conditions.
In any event, no special foot wear is needed. If regular boots are your foot wear of choice (as in you’ve found that’s what works well for you), then don’t change.
The snow is consolodated, melting spring snow, not loose powder. It won’t be “winter” hiking in the sense of what you’d experience in February. Up until early to mid afternoon, it’ll be firm enough that you’ll stay on top of it (unless it’s totally rotten out). The sun cups will be very uneven (trekking poles are highly recommended to help prevent falling). From about mid afternoon on, the snow will soften to the point that you’ll start post holing. Try and be off of it before then.
Very early in the morning, typically the snow is frozen solid. If you travel up the passes at this time, boots will have an advantage over the typical running shoes in that you’ll be able to kick steps more easily. Of course, waiting a little bit for it to warm up and let the snow soften a bit makes this a moot point.
Token Civilian