Here on our damp islands on the Atlantic shores of Europe, admission to veterinary medicine is highly competitive and it is an expensive course so people graduate with debt (though nothing like that in USA). The reality of practice life often isn’t what newly minted vets were expecting even though they have to see some practice before they even start university. It is an issue. The profession is now predominantly female and part-time working is common but staff retention can still be a problem. Hours are long, the work is physically hard and emotionally demanding, client expectations are often unreasonable, payment can be slow etc etc Burnout happens and the suicide rate remains distressingly high.
One key difference is that by law only qualified vets can treat animals in the UK. It is a monopoly. The physios, chiropractors, dentists, herbalists, spiritual healers et al have to work with the agreement of a qualified vet. Owners can not habitually get their hands on drugs to treat their horse. Vets prescribe for animals - drug safety is tightly regulated. Similarly, only a qualified farrier can shoe a horse. Successful prosecutions for illegal treatment of animals do occur. Conversely, the professional regulation of vets is tight, actually to a higher standard than for human medics, and the status of Vets is very high within the British public.
There are vanishingly few single person practices, most are multi-partner ones and most will split into “small animal” or “large animal” though many rural practices will still do some of both. Increasingly, there are practices that are specifically equine. Behind the general practices are a network of highly specialised referral practices. There are several Equine Hospitals across the country that can provide all the expensive equipment and skilled knowledge that the average practice can’t afford or justify, such as safe handling facilities for equines and the specialist veterinary nursing and technical support that leads to good treatment outcomes. University vet departments are a part of the network of referral practice: often people work in both, there is a lot of cross fertilisation.
It is a balance of owners travelling their horses to the local vet for routine work or practices covering particular areas on particular days. In emergencies, it is often quicker to travel the horse to where it will have the best care. Being the UK the distances are not as large as in the USA but it still might be a couple of hours to a specialist equestrian hospital. Where there is a concentration of horses, such as a riding school or stud or racing training yard, the vet, like the farrier, will come on a regular rotation to deal with routine matters. Vets may be employed full time by big breeding or training facilities. Emergency call outs to a stables do happen, obviously, when necessary but I suggest they are not all that common: there is generally a good working relationship between owner and vet and clients tend to ask for advice and help fairly early. They don’t expect to treat their horse themselves.
When it is necessary to put a horse to sleep, an alternative to the vet is the local hunt, who also do a professional job.
For farm livestock, veterinary medicine has moved away from reactive procedures to proactive management of welfare and biosecurity because good husbandry is very necessary to make any money in meat and milk.