I would do exactly what the folks above said if you can. However, I would not sweat it too much. I have an indoor setup for starting trees from nuts/seed under lights in a root pruning container system during the winter. I like to experiment with different techniques. Sometimes I stumble across something. At any rate, last year I ordered 50 M111 from Washington state where they are the earliest available. It might have even been December when I got them. I had ordered scions from GRIN. I collected a few scions from my own trees and grafted and potted the trees and put them under lights. I probably let them sit in a cold room for a few days first. As soon as my GRIN scions came in, I grafted and potted them.
I wanted to see if the early start, indoors, would advantage the trees. I don't think it was worth the effort. I had fairly good success and most of the failures were due to my poor grafting technique.
I did something similar this year. I only did a few trees. I got m111 a week ago and grafted about a dozen trees. I potted them immediately and put them outside. Our monthly weather report here said there might be one or two night time lows close to freezing before our last frost date. Since this is clonal rootstock and there is no tap root to prune, I put them directly in 3 gal RB2s. I'm sure on my deck, the medium will keep the roots from freezing given the projected temps. So, I did not allow any special healing time.
Time will tell how things go this year, but based on last year, I'm expecting good enough rates. I will baby these in containers on my deck for a season before planting them at the farm.
So, what the guys above have said is the best advise for "best practice". It will maximize you success rate. I'm just saying the most important thing is to keep the roots moist and the trees cool. One way to do this is with a 5 gal bucket full of damp sawdust or similar medium. You can then take a kitchen plastic garbage bag, cut a hole for the stems in the bottom and place it over the bucket. A piece of masking tape will hold the bag fairly tight to the stems. Then put it over the bucket and tuck a little in the bucket so condensation drips into the bucket, not out. Don't let the roots freeze hard. If your basement is below 50 degrees (40 better) they will be fine. If it is too warm and your garage too cold, you might consider trying a little heat around the bucket. Perhaps a large cardboard box with a hole cut out for the bucket could trap some air. A 100 watt light bulb can give off a surprising amount of heat. Make sure you rig it so the tops sticking out of the bucket stay cool and there is just enough heat in the box to keep it from freezing.
Best of luck,
Jack