You are allowed "fair transit" through the Peoples Republic of New York. You need to look around the web and find the state gun laws. It is on the NRA web page, I believe.The law is pretty clear, the firearm must be stored in the trunk of the vehicle, in a locked case and seperate from the ammo. I do not remember if the bolt had to be open or closed. I'm an expatriate New Yorker and traveled all over the state with firearms. Even got pulled over a time or two. One thing is that New York is a "declare" state. You are obligated to inform the cop that there is a firearm in the vehicle. Like I said, I was pulled over a few times, declared, told the cop where it was, sometimes they wanted to see it, some times they didn't. They do get real jumpy about handguns, so travel with them in a locked box.
If you haven't done anything to raise the cops attention, you will have no trouble. If you act like a confrontational fool, especially if you were pulled over for speeding or violating some traffic law, you can be in for a rough ride. Can they take your guns? Yep. Can they charge you with illegal possession, maybe. Unless you were using or transporting the gun in an unlawful fashion. If you keep to the interstates, stay out of the big cities like NYC or the other southern parts of the state, you will find more cops to be okay with the guns.