This is important, in case radiographs need to be taken. Show the veterinarian the horse's stall and pasture. If your pasture is too wet, or the horse always stands by a gate or under one tree, you can put down straw, gravel, or shavings to absorb the moisture in that area. You also might need to confine the horse where it can stay dry. Medicating a dirty foot is futile.
Horses throw shoes all the time.
It is better to throw a shoe than to have a too-tight shoe hurt his foot. You are doing the right thing to get help for your horse.