Yes, that's normal. I cross the border here all the time and occasionally on the Canadian side my vehicle is searched. Sometimes it's because it's just my turn and sometimes it's because I've picked up loading components. I don't believe I have ever been vehicle checked returning from Montana from hunting. Maybe, but rare. And I return "home" every year to hunt. They always ask what I am bringing back and if the guns are unloaded. And of course they want to see my gun license. Don't believe anyone has asked to see my hunting license. Usually birds are in the cooler in carrier on top or on the hitch. They often ask how many and I explain the possession limit. Deer meat stays behind to be processed into sausage and shipped to the border later.
Only once was I hassled about guns and it was my fault. My brother shipped a shotgun to me and I drove down to pick it up. Happened to be trap league night so I took my regular shotgun and ammo along because the club would be on the way back home. At the border the young guy working the window asked me if I had anything to declare and I declared the shotgun I just picked up and produced a bill of sale. "Oh, a Citori! Those are nice." Turns out he hunts birds and didn't even know there was a shotgun club in the area. Okay, I have to go in to pay the sales tax etc. Fine, but I'm met by a young guy and gal agent as I'm walking in. They want to inspect the vehicle. I smiled "Oh, I mentioned guns and have an American passport." They smiled. But I've got three dogs in the vehicle that I need to get out. Fine. So I walk to the Jimmy and go to open the door. "No, you can't do that.". But I need to get the leashes. Oh, right. Okay. I unloaded the dogs and left the tailgate down. Started to walk away. "Wait, here's the keys. You'll need to unlock the cartop carrier if you want to look at the other gun." They look at each other. "What other gun?" Oh shit! Got to yacking with the guy at the window and forgot I had the trap gun in the car and didn't declare it. Bringing an undeclared carton of cigarettes across might get someone in a little trouble but an undeclared gun is a whole lot of trouble! They did their inspection, checked serial numbers and found the 50K of coke hidden in the seat

. I waited inside. "You know, we could confiscate that gun." Yes, and that would be appropriate under the circumstances. Then I'll drive home and return with the bill of sale. I also have a ton of old photos on my phone that support me owning the gun for years. "Okay, let's see some of those." They clearly enjoyed looking at a decade's worth of hunting photos. "Good enough. Sorry to be a bother." No problem. My fault. "Just don't let the guy at the window get in trouble for not asking me if I had any other guns." They agreed all swept under the rug. I paid my duty and that was that.
The agents on either side do not want you touching or near the vehicle while they are doing their search, for obvious reasons of personal safety. Also to eliminate a lot of belly-aching while they are trying to do their job. Looking for smuggled guns is a big part of their job because we have a big problem with illegal guns coming out of the US. It's a fact. Is what it is. I don't like gun smugglers or drug smugglers and happy to put up with any personal inconvenience to help stop it. I look on it as my civic duty. Like paying taxes.