I’d normally have the shoes pulled off to make it easier to manage but that would be an “it depends”
I’d open the hole if there was obviously one there to ensure its providing relief and draining. I wouldn’t go probing though.
To keep the hole open, I’d hot tub soak twice a day for a minimum of 10 minutes to attempt to draw it and poultice if necessary until its drawn. I use epsom salts or just salt in the water.
After soaking I use a syringe filled with water that has boiled and then cooled a little and salt or epsom salts and flush out the hole/cavity area and with a really good blast. I’d then syringe flush with iodine.
Or if there’s a good hole or track I pack it with a drawing poultice paste made with icing sugar and iodine twice a day and its hot soaked in epsom salts prior to repacking to soften and remove the poultice and any gunk abscess infection. This poultice paste encourages any infection to draw out rather than be retained helps with he aim to heal it from the inside out and not for the hole to seal on the outside and keep any infection within the hoof.
Then I dress the whole foot with padding, elastowrap and a baby’s nappy (diaper) and if I’m going to turn the horse out then I put a rubber poultice boot on.
I don’t use antibiotics.
Once its all drained and clean if there’s still a hole then I’d pack with cotton wool and stokholm tar until its all healed up. Its at the stage when the pus has finished draining that ordinarily the shoes would go back on - and dependent on where the hole is - a shoe so the hole can still be accessed so it can continue to be packed. Might consider a hospital plate shoe if that was necessary.