This is something that is perfectly reasonable to do with a glass of wine. There is no reason to hurry to drink it. It’s not like ice cream. It’s not going to melt. And unless it’s like, champagne or a white that really needs chilling, which seems unlikely in Denmark in this period before refrigeration or iceboxes, it can only be made better by sitting for a bit. Claudius trying to insist on Hamlet having a drink in the middle of an athletic event could be seen as suspicious by anyone looking for it. I mean – we know why Claudius wants Hamlet to drink that wine and it IS suspicious. Wine is for spectators not athletes.