As the mentor on my team responsible for shipping across the Canada-U.S. border, I strongly recommend you read the entire shipping document sent by FIRST/FIRST Canada. The shipping rules are tedious, and might seem arbitrary, but trust me - you don't want to have a hold up at the border over something that might have been easily preventable.
Quick version, reiterating what some have already said - plywood/MDF is fine since it is "processed" wood, and can't harbour any little critters that they don't want coming into the U.S. Any dimensioned lumber is a problem, however - your standard 2x4s, etc. aren't supposed to be brought across. This includes anything that you use to construct your crate, which you mentioned was already shipped, so hopefully it got through ok. We built a new crate this year out of just plywood and steel angle on a plastic pallet, all bolted together. Remember, just because something didn't get caught
this time, doesn't mean it'll get through in the future.
You can buy wood that has been treated and is approved for cross-border shipment - someone already mentioned that this is what they usually make pallets out of. I've tried to find it for purchase in southern Ontario as just planks, but it is not easy, and it is not cheap. It must bear a specific mark to let the border inspectors know that it is allowed across, so it would have to remain on the wood that you use - see the following link (it kind of looks like a tree branch and contains code letters next to it):
http://internationalshippingusa.com/ispm_15_rules.aspx
If you can avoid all this by using a different material, I would suggest it. You certainly might be able to completely get away with it, but I personally wouldn't want to take that risk.