Equinoxes are days of balance. If the good clerics don't have power, the bad ones won't have them either.
Of course, if you wanted to destroy some "good" clerical people, I would make sure that assasins, ruffians, and poisons found there way to the good people (or people protected by good people) on this day.
Also it is probably the assasin's equivalent of "the day before christmas". Without healing magics available, people can be killed with greater ease, as you don't have to worry about clerical healing.
Solstice - Winter should be the strongest "evil" cleric night. Just like Summer Solstice is strongest for "good". Minimal modifiers either way I would think.
Aside: One of the reasons that "good holy days" were originally assigned to the solstice was to "seal" those days for good. That holy days was eventually shifted away from the Winter Solstices, because of religious calander reform AND they no longer believed in the power of the solstice.