Mom......a bit late since you posted this question and I hope your boxwood plants are safe .
Whenever plants are moved, their roots are disturbed---which can be a bit unnerving on their system---they want to protect themselves and sometimes they'll put out fresh growth or begin budding.

The plants are undoubtedly dormant now---not growing--and not likely to start---but if placed into an environment that causes them to think they should, that's when trouble starts.
The best place for dormant plants is out of the cold---but not where growth will be initiated.
One good place to put plants that have been dug up and potted, is amongst the foundation plants---next to the outside wall--there, heat (yes heat will come through) keeps the area there a bit higher than the rest of the area and is enough to prevent frost from touching the plants.
Otherwise....in the ground, then mulched heavily with leaves, soil, boughs....
what you don't want to do is place burlap or other wrap around the plants that touches them....frost then has a way to affect the plants....leaves/needles...
So keep wrap away from the plants by putting a cage around them.
Another good place is in the garage---out of the cold and away from cold drafts such as when the garage doors are opened. Again, wrapping them lightly --but away from the needles/leaves/wood.....will do nicely. Potted up, they should be given light waterings---nothing to suggest they are growing....just enough to keep the roots from drying out.