I mean the whole thing. A rink with two locker rooms (or two rinks with four locker rooms), 3-4 rows of seating, cooling system for the ice, the tech needed to operate the place, the Zamboni, etc.
You can opt to only have seating on one side to make the place smaller. Remember that from a construction point of view, the roof construction is expensive since you need really solid steel rafters since there are no pillars. Just making the building say 15 feets wider can exponentially increase the dimensions requirements for the rafters which is a significant part of the cost. Would the rink be built at a place where you can get a lot of snow?
Would advice to have 4 locker-rooms even if there only is one rink, since if there is a game two of the lockerrooms will be occupied at least 45 minutes before and 45 minutes after the slot they have booked the ice for. Maybe 3 could work if games never are back to back?
When they put up practice rinks next to a bigger rink they can make it pretty cheap, but often they piggy back of the lockerroom and cooling system of the bigger rink. My very raw estimate is that 3.5m would get you a solid building. In the long-run, the 4m building would probably be a better option. And you can scale down from 3.5m to probably 3m or less by opting for the cheapest options. I could be a little high though.
Not sure how much costs are differing between Sweden and the US, but over here I know that most smaller rinks are run for around 200-300k per year exclusive of salaries.
NYR Viper- Have it become common to export heat form the rink during the winter to nearby buildings? I know some rinks here in Sweden that gain a buck on that winter time.