Under your circumstances, I would do what I have done when I lived in the mountains of Colorado with extreme temps like yours.
I would make a poultice of Betadine and sugar. I would make it into a paste, wrap it with plastic and tape it in place with gray duct tape. Then, I would follow the horse's temperature. If he is still harboring an infection, his temperature will stay a little elevated as will his white blood count. If his temp stays up, then you will have to figure out a way to soak it, flush it with antibiotics and then wrap it like I suggested.
Hope this helps.