You do not want to try to propagate trees using branches. Only tender tips. What is your zone MiniMe? This tree should do fine in the winter without covering. The more snow the better the insulation the better it is for all plants.
I would prune these branches off your tree...cut from beneath the branch so the bark below doesn't get stripped off. Use alcohol on your sharpened pruners or pruning saw. Lovely little tree.
It will be a bit asymmetrical for awhile. Let's see what buds decide to grow after this accident before doing some pruning. See the two lower leftish branches about the same diameter? One of those is redundant. I would probably cut the higher of the two to make more air and sun for the other branches and leaves. The branch on the right side going up off the picture at the top right..see the branch branching off below that branch? That should go. Would love to walk you through a bit of pruning.
Get rid of those broken branches.
The other thing this little tree needs desperately is a tree circle around the base of your trunk. You need to remove those weeds and make sure your tree has not sunken where the soil is on the bark. Have you ever used any fertilizer? Not compost, but fertilizer? I see a bit of a circle I think but needs to be at least twice that large.
Make another question and send pictures of the entire tree from different angles. This particular species can get a lot of weight out on the end of the branches...I can see the mass branching before it goes off the page.
Your tree made it because you did not have it staked. I see the wood stake there, was that what is was for? If so when did you remove the tie downs? Staked trees are made weak. So good job!
Sweet little tree, MiniMe.