I would let them get up to outside temp, this isn't hard to do, just take them out of the cold storage and let them sit out while you get everything ready to go and prep the rootstock.
By that time they should be warm enough.
For good grafting you want the sap to be flowing up into the tree.
That means you wait for the leaf buds to start opening, not the flowers.
After the leaf buds start opening, you have a nice long window for grafting.
I usually don't graft once summer arrives.
I just graft them straight out of the fridge. Optimal dormant grafting time can vary with species, but I'll graft dormant grafts whenever I get to it after the very hardest freezes. Grafting onto dormant stocks is fine. If it's not growing the grafts have time to heal up and get ready for the bud push. It's also fine to wait though and you can even dormant graft onto actively growing trees. What you don't want to do is miss the main growth push altogether or your new scions may not grow very much. Very late grafts done in early summer may heal, but then either stay dormant or grow only a few leaves. Usually they will grow the following year though. If you graft way too early, the scions could suffer freeze damage. Healing takes place faster in warm weather as far as I know, though I'm sure there may be an optimal temperature range, I don't think it matters for homescale grafting. But that doesn't mean that slow healing won't take place during cold periods of the year. Our scion exchange is in early Feb. and I've grafted new stocks and worked stocks onto trees immediately, planted them out and had them go through snow and multiple freeze cycles and come out the other end great. Very hard extended freezes may be another matter, but when those are over, I've done pretty well no matter what with a lot of the standard fruits. The potential advantage of grafting early is that when the tree pushes, enough healing has already taken place that the scion can start growing out of the gate with the rest of the tree. I have a 10 part video series on dormant grafting if you want to geek out on it.