SKAERSOGAARD, Denmark — On a mild autumn morning, Sven Moesgaard climbed a sunbathed hill and inspected an undulating expanse of neatly planted vines. A picking crew was harvesting tons of hardy Solaris grapes that he would soon turn into thousands of bottles of crisp white and sparkling Danish wine. A decade ago, winemaking was regarded as a losing proposition in these notoriously cool climes. But as global temperatures rise, a fledgling wine industry is growing from once-unlikely fields across Scandinavia, as entrepreneurs seek to turn a warming climate to their advantage. “We’re looking for the opportunities in climate change,” said...