Sorry, I've to correct my question. I just read that the general himself in his memoirs mentiones one brief occasion.
The background is that I was fascinated reading the sentence "General...?...only visited the White House once. That visit occurred BEFORE the CW (=hint #1) broke out. I couldn't really believe this at fist and checked the other generals (If I forgot one - the question is about one of the main generals!), they all came to Washington more than once during the war. But I was a bit too superficial about checking the sought-after general. So I must add "just once", and this should be correct:
Which general met with Abraham Lincoln in Washington during the war just once?