First, get clarification from them:
Do they allow items made in a nut facility, or must the items be in nut-free facility? (You'll commonly see text, under the ingredient list on packaged food, that says "manufacturer in a facility that uses nuts" or similar text). That can make a big difference in what's available.
Then, for store bought items, check the ingredient labels--that is the safest way to go.
Stay away from M&Ms, though--every package I've ever read says "may contain peanuts" and that is a big red flag.
I bought stuff like little packages of Nerds/SweetTarts, etc. (They came in a big mixed bag).
There is a brand of snacks called "Enjoy Life"--I don't know if they make Halloween specific treats, but they are nut free, egg free, and soy free I believe. Here's the website, which I think also has a locator so you can find a place that sells their stuff:
http://www.enjoylifefoods.com/