Edit: Stella Borealis sends report that the Diocese of New Ulm is being raised to a Minor Basilica. It is an honor and allows for great feasts and special indulgences. Although there is some interest and the Polish Cathedral, St. Stanislaus Kostka, is quite beautiful, there must be some reason why they've been so honored. In search of an answer here are a few details. Winona is quite large.
Presently, there are 130,527 Catholics living in Winona on paper, according to Wikipedia, and although it has an impressive 12 men in the seminary, according to its website, none of its seminarians are attending St. Paul Seminary, which is about an hour's drive to the north, although three of the senior seminarians are studying at Sacred Heart in Detroit.
Winona is showing a flowering of vocations. Try comparing that to another, much larger Diocese, like Paris, France. Paris has 70 Seminarians as of last year, and while it has 17 times the Catholic population at 2,200,000, does not have much of a seminary. In fact, Catholics have declined in number significantly since the Second Vatican Pastoral Council.
Immemorial Mass of All Ages that his Lordship, Bishop John Quinn said recently? Perhaps competition is good for the Diocese?
The competition comes from the steadfast Society of St. Pius X, which also has a seminary in Winona, which got 20 new candidates this year.
Put together, the two Seminaries, the one Diocesan, called Immaculate Heart of Mary, and the other run by the SSPX, St. Thomas Aquinas, could easily give Paris, France a run for its money.