Except that as soon as I looked ahead, to the settings where they would stay, that was impossible. Too many green and growing things, too little snow (like, none).
Not to mention that gadding about in the outside in a way that would rather change the plot. Like a character being left unconscious on a hillside has rather more implications if it's below freezing. Like, fatal.
So -- a term right after Christmas?
No, two boys are gadding about in a way that would get them at least cold and wet in a way not contributing to the plot. It will have to be a term that starts in spring. Early spring would work, with the trees all leafless still. . .
I may have to fudge up a reason why they have to have a term each season. Shouldn't be too hard in a wizarding school where time transitions are part of the magic.