How bad is the white line? If its a mild case, the farrier can trim alot of it out and expose it to air without too much trouble or shoes. Air is the enemy of all hoof nastys so you want to pick clean and treat the feet every day.
Ditto scrubbing with dawn dish soap. I just put it in a spray bottle and scrub with my hoof pick brush and use the soapy water to rinse also. No need to rinse the soap off. Its a foot.
Also Lysol works very very well and is a bit stronger if you feel you need a bit more umph. Plain yellow Lysol women used for years to scrub their floors by hand. I have soaked feet in 1 cup of lysol to about a gallon or so of water (make it soapy) and scrubbed them clean about three times a week for really bad thrushy feet. It worked well.
There isnt much you can go about the wetness except wait it out and try to keep the feet as healthy as possible. You also may consider having a pea gravel loafing pad built where they can stand that will drain water out of it and raise them up out of the dirt. Pea gravel is very good for their feet.
GL. This year has been a bear on horse feet. Waterlogged feet everywhere.