Does snow and ice compact the soil?

Such a loaded question, Sunsanvi!  LOL

Seriously, though, it largely depends on how the garden beds are prepared for winter. If the soil is left bare, some compaction will take place and the top couple inches need to be loosened before planting.  But, if the soil had a cover crop or a heavy mulch cover over the winter, compaction will be minimized.  With cover crops, such as Winter Rye, the roots keep the soil loosened by their continued growth. Heavy mulch will spread the weight of the snow over a greater area and keep the soil from bearing the full impact. But, regardless of how it is left over the winter, if the soil has a active Soil Food Web (lots of microbial activity), they will continue "cultivating" the soil for us. "Fluffing it with a hoe" or shovel destroys a lot of that microbial activity, especially the fungi, so I don't do it unless absolutely necessary.

As for my gardens, I plant cover crops in the fall and let it grow all winter long. In spring I cut off the cover crop at the soil level and leave the cut off plants as mulch on the soil. After a couple weeks of allowing the mulch to dry, I plant among the mulch for this year's garden. I even did this during the few years I lived in Fairbanks, Alaska, and never had to till the garden.