How much head room do chickens need for nesting?

My hens nest boxes are 14 in high, deep and wide, with a 1x2 on the front to keep eggs from rolling out.

 

Do you mean nesting as in 'for the nest boxes in which they lay eggs', or do you mean roosting as in sleeping at night?

For walking-around space, and for nest box headroom, I would not allow less than 18" and that's really quite minimal IMO (for walking-around space anyhow, nestbox could be a *bit* lower if necessary).

For the roost they will sleep on, I still think it is by far best to give them space to stand upright on it (meaning, again, at least 18" for normal-sized breeds) but you can squinch down to as little as 14" if you absolutely have to.

If you live somewhere that gets Real Winter, though, and plan to winter the chickens over in the tractor, I very strongly suggest making the 'house' part as tall as possible, preferably 3-4'. (also as large square footage as feasible). Reason being, it is hard enough to winterize a tractor and maintain good air quality and healthy living conditions in there, in a cold winter... if you can't vertically separate the ventilation from the chickens, and have a truly tiny air volume, it gets REAL hard, meaning 'hard on the chickens' as well as just hard for you to manage.

If you live somwhere perpetually mild, or will have separate winter quarters for the chickens (which really I think is much the preferable option for tractored chickens in the north), then that doesn't matter as much.

Good luck, have fun,

Pat