2001 Mercury Grand Marquis

I just had studded snow tires put on my car to get ready for winter. Now the handling is ” squirrely”, all over the road at highway speeds. I asked the tire dealer about this and was told that it is because I still have the all season tires on the front. I was told that if I put studded snows on the front as well, it would alleviate the problem and enhance the car’s handling. Is this true?
Thank you2001 Mercury Grand Marquis