There is no two ways about it - horses are expensive! I run mine quite cheaply because I can keep mine out all year round and keep two out of three barefoot but I feed two bales of hay a day in winter which will cost me £12 a day this year. On top of that I have to pay for: farrier every 6 weeks, dentist, vets for vaccinations and/or illness and injuries, rugs, tack which always costs loads etc. and then you have to pay for the horse. I'm sure there are many essential things I have forgotten!
The point is that horses are very very very expensive animals and it may be quite harsh on your parents (I'm assuming you're quite young and living at home) to ask them to take on such a burden. Nothing can stop your pony from getting kicked in the field or randomly getting ill and believe me when I say that vets cost a bomb!
Sorry, I know this post may be quite depressing for you but there is no way of running horses extremely cheaply. Perhaps you could ask your parents for some riding lessons instead? If they say that those are too expensive, a pony costs many times more than that
