I keep a highland pony at full livery.
For the un-initiated, this means he's a very good doer (someone up thread mentioned this - it means he lives well on very little food) and lives at a stables where the (excellent) staff take excellent, full time care of him on my behalf. Even so, my livery fees are £450 per month - which is quite cheap by some standards - can be much more in more expensive areas of the country.
He's not shod, so the farrier trims him every 12 weeks or so at £35.00 per time - shoes (every 6 weeks or so) are £70-85 per set, depending on where you are in the country and your farrier.
Full livery is a good option if you have no horse knowledge as (with luck) you'll end up on a yard where the horse will be cared for by people who know what they're doing. (This isn't always the case, however, so check the place out thoroughly first). Other replies have detailed all the other expenses, but, to me, your biggest stumbling block is your lack of knowledge/interest in horses OP.
You do need a basic level of knowledge within the household in order to make informed decisions and deal with instances where the horse may become ill or injured (they're shockingly fragile!!) and need a vet, physio, dentist or any one of a number of other professionals to help it. My vet charges £45.00 just to arrive at the yard - that's before he's got out of his car: it's another £35.00 for him walk to the stable and pat the horse on the nose. After that just think £££££££££.
If you keep it at a DIY type yard you are committing yourself to going there twice a day, every day, rain or shine, regardless if it's christmas, your birthday or you want to go on holiday.
In short, horses are amazing things but expensive, time consuming and heartbreaking in equal measure. Unless you, your DH AND your DD are 110% committed to this level of care and upkeep, putting up with the mud, the expense and the emotional stress, please, please please do not even contemplate getting a horse.