First of all, Dumbledore did NOT tell Harry the full truth (SHOCKER, right?). He didn't actually see "himself holding socks" as the main part of an image:
Allie: What did dumbledore truly see in the mirror of Erised?
J.K. Rowling: He saw his family alive, whole and happy – Ariana, Percival and Kendra all returned to him, and Aberforth reconciled to him. (source: J.K. Rowling Web Chat Transcript Jul 30, 2007)
Now, whether he wears socks or not is unstated, but based on the rest of the answer, I would posit that yes, he does.
I would say that he did NOT outright lie (from a certain point of view :), and the socks answer was a way he hinted at the truth:
The rest of the quote explains it:
"I see myself holding a pair of thick, woolen socks." Harry stared. "One can never have enough socks," said Dumbledore. "Another Christmas has come and gone and I didn't get a pair. People will insist on giving me books." (Philosopher's Stone)
What Dumbledore wants isn't really socks. What he wants is family - someone who will give him comfortable socks for Christmas and not co-workers or associates who will give him books.
Interestingly, we could surmise that this is what Dumbledore actually meant purely from the books, without JKR's interview quote above (as proof, edit history will show that I posted this part of the answer before I remembered about the interview :)
JKR hints at the truth in two other places, and the first one is why the "Christmas" thing was important in the PS quote:
JKR makes a big deal of Harry getting clothes from Mrs. Weasley:
...'My mum. I told her you didn't expect any presents and – oh, no,' he groaned, 'she's made you a Weasley jumper.'
Harry had torn open the parcel to find a thick, hand-knitted sweater in emerald green and a large box of home-made fudge.
'Every year she makes us a jumper,' said Ron, unwrapping his own, 'and mine's always maroon.'
'That's really nice of her,' said Harry, trying the fudge, which was very tasty. (PS)
And this is an annual tradition she puts in in all the books.
JKR always goes on about how special it was for Harry to be treated as family by Weasleys (especially at the end of GoF). Being given cloths for Christmas is a family tradition. Something Dumbledore would severely miss.
Dumbledore lets on to Harry that the main reason he basically killed himself (accidentally - by putting on the cursed Resurrection Stone before Year 6), was because he longed to see his family:
"When I discovered it, after all those years, buried in the abandoned home of the Gaunts – the Hallow I had craved most of all, though in my youth I had wanted it for very different reasons – I lost my head, Harry.
I quite forgot that I was not a Horcrux, that the ring was sure to carry a curse.
I picked it up, and I put it on, and for a second I imagined that I was about to see Ariana, and my mother, and my father, and to tell them how very, very sorry, I was...
This pretty clearly establishes what his deepest desire was, which is what the Mirror would show.