I know you’re using bareroot so I’ll answer to that. You can group them and stuff them in rubbermaids. I can get 50 of those larger Missouri State pecan/walnut seedlings in a tub.
And depends on the climate of course but you can take them to a garage in a tub. If you’re in zone 4 or 5 you need to make sure the roots don’t freeze like an ice cube would be the only concern I could think of. I don’t like to winterize in my zone 5b garage because it’s really cold in there all winter. You know if you had 5-gallon rooted figs or trees or other I wouldn’t be concerned, but, non-rooted bareroot seedlings aren’t going to be as hardy.
Of course refrigeration would work great. That’s how nurseries hold bareroot seedlings all winter for us.