Well green beans would be on my list..they need to be direct seeded and I don't think corn is good to WS either.
Joann

I don't know if there are seeds that shouldn't be winter-sown, but there are some seeds that are simply easier to direct sow. I direct sow large veggie seeds like beans, cucumbers, and squash. Also rows of veggies like lettuce, carrots and beets. I scatter the seeds for some herbs like Dill and Cilantro, or let them reseed, and grow them in between perennials.

Some seedlings don't like to be transplanted and do very well by scattering seed, like poppies or larkspur. I also direct sow a large patch of tall Zinnias every year, and that works great.

Pole beans and corn both reseed in my garden. Sometimes pole beans sprout in the lawn--I think these may be unfound squirrel deposits.

Is there anything which should not be WinterSown?

Yes. Do not winter sow seeds of plants from the the tropics. Sub-tropical is fine to try if you sow towards the end of Winter, but tropical seeds don't fare well in a temperate winter.

I have WS green beans & corn successfully, but have had trouble transplanting onions of any kind that I have WSed - they just seem to keel over and die. I didn't have so much trouble with WSing alliums when I lived up north, but here, I've only had luck direct sowing them.

Drippy, I do bunching onions or scallions and plant them out via HOS, these types don't seem to mind the crowding and don't wither as much after transplant.

Thanks, Trudi - I tried small hunks, but maybe they were just too small. I love bunching onions/scallions, and you & I are in the same zone, so I will give it a shot this spring. I might actually be able to get some winter ones in down here, but not tonight - down to 28 degrees by morning!