I don't know if SPD shoes can meet the goal. Walking on snow covered ice ... you always have to pay with less flexibility in the sole, when you want more efficient pedaling.
If you look for a bit softer rubber parts, yes there are differences.
I have boodun SPD shoes. I like them. They provide atop lacing and I use them for commuting..i have no issues with slipping when I walk.
But i bought them -- my model came with nylon sole and 2 atop knobs -- for roughly 55$, since then they increased their prices a lot. I wouldn't buy them now. Good shoes but it's possible to get similar quality in sales here.
I own a pair of Santic Road shoes. The small rubber patch on the heel is very slippery. I don't know if this is the same for Santic SPD shoes. Besides that, very good shoes, I am impressed.
I tried a pair last summer which was around 40- 45$... because they looked so nice..i don't know the brand name but they are sold in a bunch of shops and have a noname lacing system.. those shoes were trash. The sole was so soft, that the cleats under the shoe were very uncomfortable.. don't recommend them. "Luckily" they were so low level that one of the threads was already destroyed when I tried to fix the SPD plates in the shoe, I got my money back from Ali .. (they were combi shoes and the SPD plates were rattling when the SPD SL cleats were mounted).
