I might part-insert it in these very cold conditions, but it is there for adequate ventilation from the bottom. With a 14 x 12 or a National brood and super, no real need at all as bees can move higher, if necessary; in a single standard brood, I'm not so sure.
All of my 14 x 12s have open OMFs.
So your tray needs removing for our normal UK weather but perhaps only partially removing for this exceptionally cold spell. All of the above is providing you do not have top ventilation. Top ventilation could change my views on your hives, but not greatly - only in that it is not required.
Regards, RAB