The question of whether rabbits that had horn existed or not is not an issue since what you see on photos is nothing other than taxidermic trickery. They do not exist.
An issue that closely related to these illustrations of the 13th to late 18th century could be the fibroma tumors or papillomatosis in rabbits caused by infectious Shope papillomavirus characterized by horny warts discovered in 1933.
This virus which is at times referred to as the cottontail cutaneous papillomavirus or the cottontail rabbit papillomavirus (CRPV) is benign (non-cancerous) that affects mainly the cottontails wild rabbits but can also affect domestic and wild rabbits. However, in some instances, it can be cancerous.
Besides it, there is the oral papillomatosis, caused by a papillomavirus that is antigenically or immunologically different from the CRPV. The oral one is characterized by oral horny warts.
Both the two viruses are infectious. We will look both at the oral and the CRPV including their symptoms and how they can be managed.
Rabbit wart image
Here is an image that will illustrate to you how the bunnies with CRPV looked like. The image may be disturbing.
The CRPV virus caused papillomatosis
This papillomavirus was first noted in Sylvilagus spp., the cottontail bunny but has also noted in hares, jackrabbits as well as the European rabbits (Oryctolagus cuniculus) both domestic and wild ones The growths it causes as already mentioned can be malignant and the virus is spread by mosquitos, ticks and other bugs.
After transmission, the virus infects a rabbit’s follicular cell and a red swollen spot will be noted where the infection occurred. This will be followed by a circular papilloma formation. Afterward, it becomes a horny wart that is keratinized with a greyish or black outer discoloration.
These born-like or horn-like growths made of vertical tissue strands are common on the head, shoulder and neck areas especially on areas without fur such as ears on eyelids.
However, the born-like protuberances can also be found on any other part of the body including the belly, and anal regions.
When on the anal region, this papilloma will slightly show different signs as opposed to cutaneous ones (affecting the skin). The rectal ones may begin bleeding when they become very large.
Diagnosis is by looking at the symptoms that this condition presents. Afterward, a microscopic examination of the tumor will follow.
Treatment is by surgical excision where the affected tissue is entirely be removed to reduce the possibilities of recurrence. Other treatment options include destroying the wart by use of electrodesiccation, liquid nitrogen or laser.
Whereas some may regress naturally without treatment, about 25% of the causes may become malignant characterized with uncontrollable abnormal cell growth which will be arising from the squamous cells found on the epidermis (squamous cell carcinoma). 
Also, the squamous cell carcinoma can metastasize (spread) to other organs including lungs, lymph nodes or advance further to the liver and kidney.
The oral papillomatosis
As stated, its cause is papillomavirus that is immunologically distinct from the CRPV but is also contagious and causes wart-like growths inside the oral cavity. Being benign, it is are not known to be cancerous.
Younger rabbits (2 months to 2 years) are more vulnerable, with the domestic bunnies being the natural host of this virus and after recovery when the ulcers that the virus causes heal, they become resistant.
Finally, the oral papillomas grow slowly and they may last from a few weeks to months to over a year and healing begins once this animal develops immunity. This is when ulceration occurs after sloughing of the tumor. Re-epithelialization marks healing.
Signs and symptoms
Oral secretions that have shed cells from the wart can transmit this virus. It can also occur from the doe to kits if kits have injured or broken mucous membrane during breastfeeding. Some of the symptoms you may notice include the following:
- Presence of “small, white, wart-like growths on the ventral tongue and rarely elsewhere on the oral mucosa.”  Typically, they are 1-3mm in size but can be larger.
- During their early stages, the lesions may be dome-shaped but they will later appear cauliflower-like
Diagnosis and treatment
Diagnosis will include a histopathological examination as well as biopsies. Also, the peroxidase-antiperoxidase technique can be used to detect structural antigens of the papillomavirus
No treatment is required except treatments to help prevent secondary infections especially bacterial as well as minimize discomfort that is associated with the lesions.
Sometimes, large papillomas may affect normal eating or they can be injured and bleed especially while your vet is conducting dental procedures. Such cases may require surgical removal.