Typically warts are caused by a virus (papilloma type) and occur on all animals including humans. A normal animal will generate an immunity from the exposure and at some stage they will all drop off - month or two. Can have severe growths if immunity is compromised by stresses like poor nutition, overcrowding etc.
Some of the discussed ways will speed up the production of antibodies but the best way is to freeze a small clump with liquid nitrogen. Freeze twice for about 15 seconds and get the iceball down to skin level. Protect the normal skin with a bit of thick vaseline but don't get it on the warts you freeze. This produces an autogenous vaccine and speeds up immunity production. Some vets here have used a bit of Levamisole or BCG vaccine to further crank up the immune system but probably not necessary. You only need to target a single small clump because that is all that is needed to stimulate immunity
Dry ice can work too but you need to freeze longer. Water ice is waste of time because it is not cold enough to destroy the tissue and release the virus particles to react with the animals immune system.
I have been enjoying reading of the cattle problems in the USA. Different, but not that much, to what we encounter here in Northern Australia.