The unsightly warts on your cattle are caused by a virus called Bovine Papillomatosis or Infectious Papillomatosis. Hairy heeled warts is a different topic and not useful for this discussion.
The most common warts on cattle are found all over the body, with specific likening to the face, head, chest, legs and genitals. In appearance, they can be flat, raised, cauliflower-like, tags, etc.
Warts mostly affect cattle 2 years of age and under. Through direct contact, from contaminated equipment (halters, hay bags, gloves, grooming supplies, etc), or even through biting insects. Once it hits your herd it is very difficult to stop it going through all of the cattle without antibodies to the virus. The virus itself lives in the wart, and is not circulated in the cow's bloostream. That is why the immune system doesn't react right away. incubation is typcally 2 months before warts start to appear, in the cow with no antibodies.
Prevention really mostly involves good biosecurity and insect management. If you take your cattle to the vet for treatment or even if they come to your property, be mindful of used equipment that is not yours. Halters, ear taggers, tattoo guns, head gates etc. If they were not cleaned from the last time used, you could be exposing your herd to warts or other diseases. You can vaccinate your herd, with the wart vaccine, but that is only partially effective, if there hasn't been a prior infection.
Most breeders will tell you that the warts will dry up and fall off in a few months, so just leave the cow alone. Sometimes the cows will drag on longer than normal and their immune system needs to be stimulated. Ask your vet on ways they recommend to do that. Some breeders inject the vaccine to spike that immune response. Some breeders will do more untested things like, cutting off or crushing the wart to see if that causes an immune response. There are topical creams one can try as well. You should also ensure that your mineral program is providing your cattle with good mineral support, which is a vital part of a strong immune system. My farm vet told me, “ It's just a skin condition, just like kids get warts when they are young. Their immune system will eventually get tire of it and will fight back.”
In Texas, many state-inspected processors will not accept an animal with warts. Depending on the infection level, they may even condemn the carcass. This is something to ask before hauling a Dexter to their appointment. Another complication is the risk of secondary infections if the Dexter gets a bad case of warts. They can invade the eye area, genital region and bleed when getting rubbed on things.
Above: Small very movable ( tag-like) wart deep in hair.
Above: Cauliflower type wart on top of head, behind ear.
Above: Flat, not movable wart on top of back.