The best way to find out if you enjoy horses is to take lessons either in riding or driving. You’ll be able to ride or drive once or twice a week and may be able to buy or work (usually mucking out stalls) for practice time.
Some stables part-board lesson horses, and some owners will part-board a horse to offset expenses or ensure their horse is getting exercise. You will be paying for a certain number of riding hours or riding privileges at certain times.
For a monthly fee you will have use of a horse, either in your own stable or the owner's stable. This can be the most costly option.
You might find someone who would be willing to loan you a horse. Usually these horses are semi-retired and need light riding. Sometimes owners find themselves in a situation where they can’t give enough attention to a horse but don’t want to sell. This isn’t an option to be counted upon, but it is possible if you prove yourself willing and able to look after someone else’s beloved horse.