38 - Number of players who have played for both the Capitals and their Winter Classic opponents, the Chicago Blackhawks. Per the NHL, "[o]f those 38, only one has skated in at least 200 games for both clubs – current Capitals forward Troy Brouwer (CHI: 238, WSH: 247). Brouwer played for the Blackhawks in the 2009 Bridgestone NHL Winter Classic against the Red Wings at Wrigley Field."
Here (via the NHL's Winter Classic Media Guide) is a full list of those 38 Caphawks, err, Blapitals, err... whatever:
And while the Media Guide correctly notes that no one has ever coached both teams, it's worth mentioning that current Blackhawks' bench boss Joel Quenneville played his last nine NHL games for the Caps and former Washington head coach Bruce Cassidy was a 'Hawks first-round pick who played 36 games for them.