@Travis Hobbs has provided good info.
I shot my musk ox back in 2004, so some things might have changed, but I have done other hunting trips to Canada, with my most recent, an Alberta moose hunt last year.
For both my musk ox hunt and my moose hunt last year I drove from my home in Montana to Edmonton or beyond.
On my musk ox hunt I also shot 2 caribou. I brought home the shoulder capes of both caribou and the full body hide of my musk ox, a 50# cooler of meat, the antlers of both caribou, and the musk ox skull with horns. At US Customs we had a little discussion as the agent said that the musk ox skull needed to have been boiled clean. I had to fill out a US Customs form on the meat. I knew that one of my caribou on that trip met B&C minimum, so I didn't split the skull caps on either rack and had them taped together. They wouldn't fit inside my truck camper, so I had them tied on top. US Customs only asked what kind of animal they were off of, and didn't look any further at them.
In 2007 I hunted caribou in Quebec and flew there from Denver. I didn't bring any meat home, I left the shoulder cape with a taxidermist in Toronto to have tanned and he shipped it to my home, no problems. That caribou also met B&C minimum (my avatar pic) so I didn't split the skull. I really wrapped the antlers with bubble wrap and cardboard. I flew it back with me as oversize baggage, and at US Customs I was called to two separate rooms, one to fill out the import forms, and the other where agents fully inspected the antlers and cut open the wrapping around the skull plate. All made it home OK.
Last year I drove from my home in Montana to Ft. McMurray, Alberta.
Going into Canada, I had pre filled out the Canadian Non-resident Firearms Declaration form, but it was on 8 1/2"x14" paper that my printer doesn't print, so I printed it on two sheets. The Canadian customs agent didn't like that so I had to re-fill out another form at the border. I also had to produce the contract between me and my hunting outfitter. The Canadian customs agent also came out to my car and inspected my rifle.
Coming home, I remembered the previous hassle with my musk ox skull, so I asked my outfitter what I needed to do with my moose antlers and skull cap. He said just to stop at a car wash and power wash the inside of the skull plate, which I did.
At the US Border, because I had my rifle and game meat I had to go inside and had a very long wait to finally see an agent. I don't remember if he even asked about my rifle, he didn't want to look at my coolers, or the antlers, but he had me fill out a form to bring the meat into the US, said thank you, and I was on my way.
I think that every customs agent,on both sides, handles the border crossing differently. Canada seems most interested in your firearm, US Customs are more interested in any meat you might bring home. Ask your hunting outfitter what you should to with your musk ox skull.
It takes up a bit of space, but I strongly recommend a full mount of your musk ox.