I don't think locating an owner is quite the best idea, you have no idea if they are knowledgeable or their horse is suitable. The first thing I'd do is locate a riding school and give them a call and organise a trial lesson . I'd probably recommend starting with English, so maybe dressage lessons, and switching to another discipline later on if you want shouldn't be hard. The stuff like breeds simply don't matter at this stage, stop even thinking about it. Take lessons for weekly six months, help at the stables and by then you should start to have an idea what you want.
Horses aren't dogs, they're not really companion pets. We train dogs and cats to understand our language but we have to learn the horses language. Every horse will test you and will try to get their way and be dominant, if you're not willing to stand up to the horse and demand respect then horse ownership isn't for you . As much as horses are magnificent and beautiful they're also impulsive, violent and, strong careless. Just one of the many kicks dealt out in a herd daily could be life ending for a human, and whenever afraid a horse will want to run regardless of their passenger or handler unless you learn how to be the leader. I say this because you talk about a horse as a pet, but the way we need to interact with them is different to pets.
I'd say forget about showing for now. Showing requires lots of work and regular instruction, which if you're that isolated when you move doesn't seem attainable. Horses are best in company, so two or more would be good. When you do look for a horse, don't look for a pretty one or colour, look for one that has been ridden by beginners, that is calm and easy for you to handle. You don't need a fancy horse - just a safe sone, and once you're experienced you can look at getting a different horse later on. Also, you said you'd like a cold blood, I would probably advise against that, few are bred for riding horses. A nice stock breed or riding breed will be much more suitable.