I thought Mance was asking about the crypts because he knows of a way out of Winterfell through them.
However, he did volunteer to go to Winterfell so it makes sense he would have another ulterior motive to going. If the horn is there, I'm not sure it would actually make the Wall collapse. Joramun fought against the Others so I can't understand why he would have something that could make the barrier that keeps them out of the kingdoms fall.
If the Wall falls, I feel like it will have something to do with what Old Nan said about the Wall standing as long as the men of the Night's Watch stay true. We know they murdered their last two Lord Commanders so they are not staying true. That could negate the magic in the Wall that wards off the Others.
That's the horn that would bring down the Wall, right? And they didn't want to bring down the Wall because then you have nothing to hide behind any more, right?
Why even create a horn to do that if there's Others on the other side that can invade Westeros?
I don't really get that part.
The thing is that he didn't volunteer to go to Winterfell. The girl in Melisandre's vision was near Long Lake. The location for the wedding was changed at the last minute, I believe, so they couldn't have known that fArya was actually in Winterfell. And yes, if Mance is trying to find the Horn still, it's very suspicious. I made a post a little while back about how I thought the Wall would fall. It's a little lengthy so here are the c+p relevant bits:
I know the popular opinion is that the horn in Sam's possession is actually the Horn of Winter, but I think that this might be a red herring and it really is just some old, cracked horn. I think that the real Horn of Winter is hidden in the crypts of Winterfell. I think that Mance Rayder knows this, and that this was the real motivation behind both of his infiltrations. Considering that his spearwives kept asking Theon where the crypts were located, Mance's first attempt at gaining access to them was unsuccessful. While it is possible that they could have merely served as a hideout or quick escape route should something go awry, his sniffing after the crypts doesn't make sense otherwise. It is likely that the purpose behind his excavations in the Frost Fangs was to create a diversion by finding a suitable, temporary stand-in that would be seen as a big enough of a threat by the Watch that they would let the wildlings pass, thus giving him more time to get his hands on the real horn. I think that rescuing "Arya" was never actually a part of his plan. But, why is he so determined to find the horn? Wouldn't tearing down the Wall be quite counter-productive to his goal of protecting his people?
"If I sound the Horn of Winter, the Wall will fall. Or so the songs would have me believe. There are those among my people who want nothing more..."
"But once the Wall is fallen," Dalla said, "what will stop the Others?"
Mance gave her a fond smile. "It's a wise woman I've found. A true queen." He turned back to Jon. "Go back and tell them to open their gate and let us pass. If they do, I will give them the horn, and the Wall will stand until the end of days."
I can't help but wonder that perhaps this is exactly what Mance had in mind. Is it possible that he hasn't been entirely honest about his agenda? What does he know that we don't? His fate at the end of aDwD is quite uncertain. Ramsay would have us believe that he is holding Mance captive. I think that this is a lie. It is likely that he was able to discover the details of the plan to rescue "Arya" from one of the spearwives instead, and that Mance peaced out at the first sign of trouble and sought refuge in the crypts.
I also like what Bran Vras has suggested about Mance and the Horn of Winter (TL;DR - the horn is in the cyrpts and Mance gets his hands on it; this is the mysterious horn sounding from somewhere inside of the castle before the big escape). Either way, The King Beyond the Wall has scaled said Wall countless times, has snuck his way inside of Winterfell on more than one occasion, and even gave Stannis Baratheon the slip right under his nose. If there is anyone in Westeros that is going to finally bust him, I highly doubt that it will be Ramsay Snow of all people.