The bigger the tire, the heavier car will slide in slippery road conditions

I disagree. I've always driven vans, and I've always insisted on the widest tires I could get. I want as much rubber on the road as possible. I hate those wimpy rubber band tires that are so popular and common today. Give me big old fat tires every time.

However, there IS something that does make a difference. The tread pattern. You need to have a tread pattern that deal with wet and icy and slippery conditions. Some tires are good at it, others are totally crap. I've driven in snow, rain, mud, and never had a problem with traction. The only time my vehicles have ever slipped or slid is on black ice, and believe me, it doesn't matter what tires you have in that. A freakin bulldozer would slide in black ice.

Not true !.  If it was true all truck drivers (and probably the regulatiions / law) would change to the smallest tires.....   Physics say the opposite !.  I don't want to get into it (too lond and boaring) but from the basic laws of physicas your statement / assumption is wrong / incorrect !.