Plants, roots, and tubers I ordered are already arriving and I am like HEY hold up it is still winter here... Traditionally March and April are our snowiest months... However I currently have horseradish and sunchoke here and have been notified my onions are on their way here... My plan was to put them all in large grow bags but with the possibility of at least one more winter storm between now and our last frost date at the end of May I am a bit concerned. Can I plant them out now or should I wait? If I wait how should I store them?

Horseradish and sunchokes are completely winter hardy in the ground here, so I think it is safe to pot and put them out, even if it snows.
Snowing here this morning after a night of rain... you have my sympathies!

Yes, the horseradish and sunchokes should be fine (or at least they would be in the ground; not sure about grow bags). I believe some sunchoke varieties might not tolerate cold weather as well as others, but if they're rated for your zone they should be fine.

My experience with Allium cepa onions from sets is limited. However, Allium cepa onion sets are supposed to grow best when it's above 40 degrees F., and planting in colder weather may delay growth. They say to plant them two to four weeks before your average last frost date. They're said to prefer cool, but not cold weather. However, onions are fairly cold-hardy; occasional snow shouldn't be a big deal as long as it's not too cold. Most varieties are said to be hardy to 20 degrees F., but I've read that 28 degrees F. or lower can be a problem at the end of the season pre-harvest. I've read that temperatures below 13 degrees F. can kill onions. For overwintered adult onions, your winters will probably kill a certain large percentage of them, and spare the rest.

I have had Allium cepa onions die, seemingly from cold, however (over the winter--not when starting them from seed in an unheated 6'x5'x3' tent-like greenhouse in the spring; they were perfectly fine there, even when other things froze).

I have a lot more experience with Allium fistulosum (grown from seed, and overwintered in the ground). If they're Allium fistulosum (like Crimson Forest and He Shi Ko), they should be a lot more cold-hardy (I've never had them die due to the cold, as far as I know). I've never seen those sold as sets, though (usually they're grown from seed by the gardener).

If you end up having to hold the onions for a few weeks, I suggest untying the bundle and loosening the plants so they can breathe. Last year my onions came too early, and I left them in my cold garage, in the original packing but with an opened end to the air. When I pulled them out for planting, I had some mildew and rot in the bundle. My fault for not providing better air circulation.

My potatoes are starting to sprout but it is too soon to plant them so I am keeping them in the cool garage so I would suggest that you do the same with your roots and plants.

I planted my seed potatoes last week even though the weather in Wisconsin is still cold, lows in the 30s or 20s and highs in the 40s but it was for mental health reasons. It's April and still cold out here!

Oh, one note on the sunchokes is you'll need to plant those ASAP, or they'll go bad. If you want to keep them indoors, you should keep them in soil indoors, to keep them alive.