That would actually be an interesting experiment. My bike doesn't have a front rack so I can't try for myself.

What I've found is that some amount of front sideslip is inevitable. My bike is a drop-bar CX/tourer. If I ride in the snow the way I do in the dry, with a lot of weight on the hoods, the front end follows ruts in the snow and ice. If I sit back putting more weight on the rear, the front end is still subject to a little light wander, but it's generally easier to maintain course.

Now, a lot of wight on the front may be a different matter entirely.

It makes no difference, BTW, in slush, virgin snow or smooth ice. It's only in rutted snow or ice where I experience this.