If your soil is thawed and workable you can move the rose now. However, I think maybe that's not the case yet in Northern Ohio. It certainly isn't here in SE Michigan. Even though the top of the soil seems to be soft if you dig a little further down it's still pretty frozen. But early spring when they just begin to wake up from dormancy is a good time to move roses in general. If you move them just before they leaf out they'll hardly know they were moved and should survive just fine.

I don't usually put any fertilizers right in the hole. It can burn small, tender feeder roots. Move it first and then work some slow release fertilizer into the soil around the rose once you see it begin to grow.

the soil sounds fine and yes, you definitely want full sun. Roses need 6 to 8 hours of direct sunlight to grow and bloom properly. If there isn't enough sun they may grow but won't bloom much.