It coastz mudkipz and 10 rainbowz
I don't know what the previous poster's currency is but in US Dollars you can build a stripped down (there won't be a lot of flex or extra space for other amenities or even money making possibilities) rink for less than $1,000,000 and after that, the sky is the limit. As a female figure skater interested in building my own rink, I have been looking into this for years and drawing various plans for roller and ice rinks since I was about 12 years old. My dad did commercial construction work for years and I think I have interest in drawing plans and building things from him.
Many rinks (buildings, chillers, HVAC, fixtures, etc. NOT including furnishings) fall between the $1.5 and 6 million dollar mark depending on the number of ice surfaces, square footage, grading (if any), etc. It is because of all these variables that no one will be able to give you a firm price until you've got some plans and materials lists in hand. Also, how will the rink be used? Do you want a rink dedicated to figure skating, hockey or both? Year round or seasonal?
Also, the more space and amenities you want, the higher the price will be and furnishings will add to costs so all of this must be taken into account. You will make the most money if you have a low debt load arena so keep in mind the amount of money that will have to be financed versus the amount that you will be able to pay outright towards the cost. The less borrowed, the better for you if you're in it for the long haul.