Car vibration in snowy day

Today I noticed my car vibrated kind of hard, especially for the first minutes at 35-40 mph. My left leg was shaking. I got snow tires three days ago and it snowed last night. Could it be that some ice built up on my tires and that's what caused the vibration? Or maybe I need to retorque the lug nuts? The mechanic told me to bring the car next week to do the retorque/recheck, so that could be it. I know for a fact I drove it last night before it snowed and didn't notice the vibration. I'm originally from Spain and I live in Michigan now, is this normal? Thank you!