It really depends on the snow. The amount of moisture in it, the amount of pack it has to it and the depth of it. Liken it to riding a bike on the beach. Away from the water, it is very fine and gritty and offers very little traction. Down by the water, it is more hard packed and you don't sink into it like you do away from the water. The snow is a lot like that. 4" of fresh powder with nothing underneath and a mountain bike should go through it fairly well. 4" of wet snow will be the exact opposite.

Last year I rode my fat bike to work in the snow. It was snowing and there was probably about 3-4" of fresh powder on the MUP. I was blazing along at 17mph with no issue at all. Tire pressure was dropped slightly since I wanted the added traction. I never slipped once, never lost traction, never gave it a second thought. Well, it kept snowing that day and into the night. When I rode back home 6 hours later, there was a foot of snow and it was still coming down. The snow consistency had changed drastically to a much wet and thicker snow similar to mashed potatoes. My fat tires were getting no traction at all. I couldn't manage to stay upright on the bike for more than a mile before falling. After the 7th time I went down, I stopped counting. The last mile I had to push the bike through a foot or more of drifted snow back to my complex. I couldn't even get on the bike and start pedaling at this point. The snow was too deep, and it was way too wet and heavy.