Please don't worry about this, it sounds simply like her soles are going through the normal exfoliation process. Small pieces or even the whole sole can peel away, a bit like flaky skin on humans.....
Soaking them will not make them moist. It will waterlog them which is unhealthy. Moisture content is a very fine balance and comes from within the hoof, hence why on a hot day you get wet footprints.
Once the pieces have flaked off she will have a lovely new sole underneath
edited to add ...... Most hoof oils and moists will prevent the hoof from breathing, check it is breathable, but preferably don't use.