Nut sure about turnips as I haven't grown them, but yes, the carrots are mush, or will be when the ground thaws. They don't tolerate freezing soil in my experience.

The parsnips get better after the soil thaws (here, the soil is frozen from Dec. 15 to Feb. 15). I only have experience with carrots under hoophouses, where the soil never freezes for long (one sunny day and it unfreezes). In that case, my carrots have survived several freezes while keeping good quality. No experience with turnips, but maybe they are more parsnip-like.

I thought my carrots would be compost after we had a rather (for us) prolonged deep freeze. The ground in the yard was frozen solid, but I had about a foot of straw on the carrots and they came through just fine. We pulled about 6 today and they look and taste great.

Turnips are much more susceptible to freezing than carrots. In the final analysis tho, you will not know until you try.

OK well I guess I'll just have to bundle up and get out there to dig them up. I think we're supposed to have a couple days in the 40's towards the end of this week so I'll try then. Here's hoping!

I know the answer to radishes/ turnips first hand; They may survive dwn to 20sF or so but will be perishe beyond that(in teens). I have some that are frozen right now. We had freez down to 15F for several nighs in the past week.
Carrost will become soft and mushi, like potatoes, I think.
My radishe lasted all winter last year but not this year.

Great news - my carrots are fine! I pulled them all up today (in only a sweatshirt, no less - it really got warm outside!) They taste just as good as they did in the summer.

I think the plants were actually still alive - although the green tops were damaged, today they definitely perked up and parts were bushy and green.

The turnips I'm still not so sure about - they seem just a tiny bit softer than usual. I'm still going to try cooking them and see how they taste.

Next year I'm going to add another layer of poly on top of the agribon and I think I'll be good to go.

I pile hay on the turnips and carrots and after temps below 5 degrees they're just fine. But radishes have way too much water in them. I pull the big Asian radishes in the fall.

Carrots are done here in MI after freezes.

Well, I just checked my carrots that were in frozen ground for about 3 weeks and they are fine. Very surprising.

Luke

Once the ground freezes around here your done. Only mush left in the spring. Only made that mistake twice. This year(lazy) once many years ago.

Normally i just cover with 12" leaves and I'm good to go. One year in January it was zero degrees out with a foot of snow. Carrots were fine, in fact there was some type of grubs still alive.

Today, took some soil out of my coldframe to start some spinach and low a behold a slug hitched a ride! Can't believe it.