Did the spears pull on the brownies?

Are the smaller ones that suffered, Needles, Windmills or both. Palms gain in hardiness as they get bigger, so your situation is not unusual. Leave the leaves as long as there is any green in them, even in the leaf petioles. Trachys can come back from complete defoliation--the health of the bud is essential. Do you see any green in the center of the palm (any evidence of an emerging leaf?) Definitely was a BAD winter but if the bud is still green and doesn't pull with a gentle tug, it'll survive and should refoliate shortly. Also, you might want to pour some hydrogen peroxide into the centers.--Don't feed until there is evidence of new growth though.

Don't water either you will only assist in rotting the plant. Wait till summer when temperatures are above 80. I have have seen the center trunk of a needle palm die completely. Yet suckers still emerged in spring.

they are two (2) needles and one (1) windmill that are in trouble. There is hardly any green to speak of. What will pouring hydrogen peroxide down the center do?

It will help cure the rot inside the cavity. I find it works faster than any fungicidal spray.