What should I do?

"Why don't you order your trees for spring delivery? Mrs. G"

Well fall is an excellent time to plant trees, the ground is much warmer than spring. It gives you a head start on spring for sure. I myself think it is the best time. Plus many nurseries ship in January or February like Grow Organics, or Bay Laurel. So we are in the same boat in the spring. Stark Brothers even sent my blueberries in March. I had to pot them up, the last hard frost here this year was April 25th. I kept them 7 weeks in pots, it was a huge problem, as all available window space is taken up by my plants now.
I blame the nursery as the zip code says it all, they messed up.

I guess we have to give them a date ourselves. I planted a Weeping Santa Rosa about a month ago. It looks very good, no growth of course, but the branches are very green, it's had a chance to spread it's roots and take hold and be off and running much earlier than anything you plant here in the spring.
I know Bay Laurel can wait till the first week in March, and that is late enough for zone 6a, but probably not for you in Zone 5. Stark might honor your date, ask first or don't order from them. I will not be buying anything from them this year. But if I buy in the future, I will ask to deliver May 1st.
If they cannot, forget it. Raintree, Willis, Indiana, One Green World, Edible Landscaping, all had no trouble delivering at exactly the right time.

I'd take a pickaxe and break through the frozen ground. Then if it's not too many trees, bucket the frozen ground up from the holes and bring it in a heated portion of your house (like maybe a heated garage?) to thaw. One the dirt is thawed, I'd plant the trees in the holes and fill in the holes with the thawed dirt. Tamp the soil down and the trees should do fine.

Be sure to actually plant the trees when the weather is above freezing, or at least not much below freezing. I once lost a peach tree because I planted it in sub-freezing weather. The roots can't take bitter cold air temperatures. They assume the temperature of the air very quickly and will die if it's too cold. They are much safer in the ground. Even frozen ground provides some insulation from bitter cold air temperatures.

During the warm spell you can try to catch the heat with plastic over the plots as well.

If you are planting in a sod I would be surprised if the ground is frozen solid, even in Z5. My outdoor thermometer reads 8 degrees F. right now, and though I expect it may be giving a read a few degrees low it's been pretty cold here but the digging is easy, even in bare dirt. I was digging out trees yesterday.

Drew,

Shiro is self-pollinating here. I understand self-pollination can be affected by zone (don't understand it) so it may be different in the Great Lakes area.

Plant them in the early spring when you can dig the hole.

I agree, unless this is an unusually early freeze, you should not order trees this late or from someone you cannot specify a delivery month. Let them do the worrying over winter.

Well not our area, Stark's, Grandpa's, Gurney's and Treefarm nurseries say otherwise.
I could find no reference that it was self pollinating. Just the opposite actually.
Edit:

OK, I dug further and Dave Wilson Nursery calls it self Fruitful, and Raintree says partially self fruitful.
So it looks to me best to at least have another for a full crop. But who knows?

One Green World says it needs a pollinator.
Rolling River says Self fruitful.

I got four trees planted today. Tomorrow, I hope to get all the raspberries planted.

If you don't have too many of them you can take a big heater and use sheet metal to force the heat down on the spot you need thawed. Its not efficient or fast, but it works if you only have a few to put in. When I say heater I mean one of those diesel or kerosene heaters that looks like a jet engine, 50k btu or so.