WINTER CARE- KOREAN HORNBEAM

Any thoughts on winter care for an older hornbeam? My hornbeam was in a too-shallow pot with very poor drainage for several years. Yellow leaves and many small twigs slowly dying. This tree is more than 60 yrs old, about 15inches tall with 6 inch nebari.
Did an emergency re-pot 3 weeks ago in to a larger, deeper pot. Removed only the dead roots and some of the old soil. Now placed in to a better draining soil.
My only choices for winter care are:
An unheated, enclosed porch where the temp. is 50-55 degrees regardless of the outside temps. Light but no direct sun. Or..
Outside, off the benches, next to the back of the house, out of wind and direct sun. Pine bark nuggets covering the pots.
I've had good success with trees in both places for the winter. I'm in zone 7a, 5 miles from the Atlantic Ocean. Our winters have become very unsettled--temps from 0-55 degrees, piles of snow, ground frozen and then thawing.
Thanks for your help, Lynn

At 50-55 degrees constant, your tree will not receive dormancy thru the winter. I don't know if a weakened hornbeam would be ok with that. I think I'd opt for the other location, giving it a bit of extra protection if possible, for super cold snaps.

has it been in the same general geographical location for most of its life ?

if not and it has come from a climate where it did experience full winter dormancy, it might need something that would provide a more consistent temp, like maybe a re-purposed refrigerator set to about 34-36 degrees +/-

my little blended trunk korean h-beam was frozen pretty solid for most of this past winter and is doing well (zone 5b but last winter was more like zone 3)

Judy--thanks for your reply.
Kevin--this tree has lived in this zone for more than 20yrs. Outside, mulched in during our winters. My concern is more for its depleted state and recent untimely re-pot. Should I do something different this winter?
Thanks, lynn

Can you put the tree UNDER the benches, with the pot covered by mulch, etc. (and possibly with Chicken wire around it for protection from varmints?)?

Jim--Thanks for your advice; it sounds like a plan! Lynn