Last I heard, it was going to have a retractible roof, a la University of Phoenix Stadium in Arizona. But it appears from the Twins'
Stadium FAQ page that that won't be the case. The site also says it should be finished in 2010:
The Minnesota Twins new stadium FAQ page wrote:
Will there be a roof?
The Twins-Hennepin County ballpark bill, passed by the 2006 legislature, calls for the construction of an open-air facility.
How will you provide comfort for the fans during less-than-perfect weather?
The Twins and county are considering a variety of elements aimed at providing extra comfort to fans. Among those elements are the potential for heated seats, the use of radiant heat in the concourse and concession areas and a large sunscreen sheltering the upper deck.
As jj said, follow the money.